Datasets

This section describes all B2000++ datasets. Please observe the following conventions for dataset names and dataset name attributes:

  • Dataset names printed in upper-case are fixed names.

  • Dataset name fields printed in lowercase mean that the corresponding field is variable and will be substituted.

  • Branch identifiers: br or branch means branch identifier (a positive integer). The branch identifier is either external or internal, depending on the context.

  • Identifiers: id, eid, iid means identifier. It is in most cases an integer. Depending on the context, an identifier can also consist of a string. An external identifier eid can have any positive integer value. Internal identifiers are numbered consecutively, starting at 1 (a Fortran heritage).

  • cycle, subcycle, case, subcase, mode are all integers.

Summary of B2000++ Datasets

ADIR

Analysis directives

BCS_CONSTITUTIVE_MATRIX.0.0.<cid>

Beam section solver constitutive matrix

BDTB.<br>

Branch description tables

CASE.<cid>

Analysis case descriptions

COOR.<br>

Mesh node coordinates

COOR_IP.<br>.0.0.<cid>

Branch element integration point coordinates

DOF_INIT.<br>.0.0.<eid>

Initial conditions (dynamic analysis)

DOFD_INIT.<br>.0.0.<eid>

Derivatives of initial condition with respect time

DOF solution field

Solution fields

EBC.<br>.0.0.<eid>

Essential boundary conditions

EDGESET.<br>.0.0.<name>

Selected element edges set

element-field

Solution fields defined per element, usually gradients

ELEMENT-PARAMETERS

Parameters describing element type

ELEMENTSET.<br>.0.0.<name>

Selected elements set

ELEM_IP.<br>.0.0.<cid>

Branch element integration point identifiers

EPATCH.<eid>

Description of element mesh patches

ETAB.<br>

Element description tables

FACESET.<br>.0.0.<name>

Selected element face set

FIELDS

Solution fields parameter list

IP.<br>.0.0.<cid>`

Branch element integration natural coordinates

JCTS

Branch connectivity list

LINC[.<eid>]

Linear constraints

MASS_AND_COG.<br>

Mass summary

MATERIAL.<mid>

Material descriptors

NBC.<br>.0.0.<eid>

Natural boundary conditions

NLCS.<br> Node-local transformations

Node-local transformations

NODA.<br>

Additional node parameters

NODE-PARAMETERS

Parameters describing node type

NODE-NORMALS.<br>

Node normals

NODESET.<br>.0.0.<name>

Selected node set

PROPERTY.<pid> Element properties

Element property tables

SOLUTION.0.0.0.<case>

Solution summary

SOLUTION-STAGE.0.0.0.<cid>.<stageid>

Solution stage summary

SOLUTION-STEP.0.<cycle>.0.<cid>

Solution step summary

<gname>.<br>.<cycle>.<subcycle>.<cid>

Sampling point field

TITLE

Problem title

TRANSFORMATIONS

Transformations (DOF transformations)

VOLUME.<br>

Element volumes

Summary of B2000++ obsolete datasets (V4.4)

EDGELIST

Selected element edges list (replaced by EDGESET).

ELEMENTLIST

Selected element set (replaced by ELEMENTSET).

FACELIST

Selected element face list (replaced by FACESET).

NODELIST

Selected node list (replaced by NODESET).

ADIR

The analysis directives table contains the top-level information on the problem (an array of MemCom dataset type I) . The information in ADIR is split into two parts, of which one is stored in the descriptor and the other in the data set. While the descriptor of ADIR contains essential top-level analysis control parameters and some optional parameters, the data set contains a list of the branch identifiers.

Content of Dataset Descriptor

The following keywords are always present in the ADIR descriptor. In addition, other global keywords can be added, depending on the program context.

Keyword

Type

Description

ANALYSIS

K string

Type of analysis. Optional, if omitted, a linear analysis is assumed.

CASES

I integer

Array containing the ‘load’ cases to be processed.

NBR

I integer

Total number of active and passive branches.

SYSTEM

K string

Name of program that generated this database.

VERSION

I integer

Array containing program version (major, minor, cycle).

Content of Dataset

Array of type I containing the list of the external branch numbers. The external branch numbers can be listed in any order. If a single branch is defined, its identifier must be 1.

Access

ADIR is created by the input processor and is updated as required by other B2000++ applications.

BCS_CONSTITUTIVE_MATRIX.0.0.<cid>

The beam section solver constitutive matrix contains the 6 by 6 beam section solver constitutive matrix (an array of MemCom dataset type F).

Content of Dataset Descriptor

Keyword

Type

Description

MASS

F float

Total mass (per unit length) of section.

MASS_CENTER

F floats

Position y and z of the center of gravity with respect to section FE model coordinate system.

MASS_INERTIA_MOMENTS

F floats

Mass inertia moments yy, zz, and yz.

NEUTRAL_AXIS

F floats

Position y and z of the neutral axis with respect to section FE model coordinate system.

Content of Dataset

6 by 6 beam section solver constitutive matrix stored row-wise as an one-dimensional array.

BDTB.<br>

The branch mesh description table (a relational table of MemCom dataset type $) contains the primary information on a branch, storing parameters such as the type of the mesh, the number of nodes, elements, grid lines etc.

Content of Dataset

Relational table containing the following keys:

Keyword

Type

Description

BTRF

F float

Array defining the branch-global to global-global coordinate transformation matrix (optional). The array contains the translation vector and the rotation matrix (row-wise) for transforming branch-global coordinates to global-global coordinates. If omitted, the orientation of the branch is the same as the global orientation. See comment below.

LTYP

I integer

Array containing a list with all internal element type numbers used in this model (required). See dataset ELEMENT-PARAMETERS for the definition of the element type number.

MESH

K string

Type of mesh. For B2000++ meshes MESH must be set to U (unstructured). Any other mesh types will not work with B2000++.

Access

BDTB is created by the input processor and is updated as required by other B2000++ programs.

Additional Information

BTRF defines the translation and rotation transformation from the branch-global to the global-global coordinate system. The first 3 array elements of BTRF contain the translation vector t with respect to the global coordinate system. The array elements 4 to 12 define the rotation matrix base vectors e (row-wise)

t1,t2,t3,e11,e21,e31,e12,e22,e32,e13,e23,e33

ti are 3 translation vector coefficients and ei the 3 rotation matrix base vectors.

CASE.<cid>

The analysis case (“load case”) description tables list all parameters of a case to be processed by the relevant solver (an array of relational tables of MemCom dataset type $). Such parameters are essential and natural boundary conditions identifiers (like ‘forces’, ‘heat’, etc.), links between branches, constraint equations, etc. All parameters specified by a CASE description will be combined to form a single pair of essential and natural boundary conditions. Note that the case identifier <cid> is a positive integer.

Content of Dataset Descriptor

The descriptor contains all parameters common to all components of the case.

Keyword

Type

Description

DOF_SOL

K string

Name of equation (DOF) solution dataset to be generated for this case. The name is usually of the form <gname>.*.*.*.<cid>, where gname is the generic name of the solution, such as DISP or TEMP, and <cid> is the ‘load’ case identification number.

GRADIENTS

I integer

Gradient computation flag. 0 means no gradients computed, 1 means gradients computed, and -1 means only last solution step gradients computed.

GRAVITY

F float

Gravity acceleration vector \((g_x, g_y, g_z)\). If no gravity has been specified this key is not defined.

NBC_SOL

K string

Name of the natural boundary condition set to be generated for this case. The name is usually of the form <gname>.*.*.*.<cid>, where gname is the generic name of the solution, such as FORC or HEAT, and <cid> is the ‘load’ case identification number.

RCFO_RESTRICT

K string

Type of reaction force restriction (if applicable, i.e. defined in the input). Values are Force or EndShortening.

RESIDUUM_SOL

K string

Data set name of the residuum set to be generated for this case. The name is usually of the form <gname>.*.*.*.<cid>, where gname is the generic name of the solution, such as RCFO or RHEAT, and eid is the ‘load’ case identification number.

STEP_SIZE_INIT

F float

Size of the initial load step. Defined during non-linear analysis only.

STEP_SIZE_MIN

F float

Size of the minimum load step. Defined during non-linear analysis only.

STEP_SIZE_MAX

F float

Size of the maximum load step. Defined during non-linear analysis only.

TITLE

K string

Optional short description of the case.

Content of Dataset

One or more of relational table sub-sets, each of them describing a component contributing to the current case:

Keyword

Type

Description

NAME

K string

Name of component. Currently, the following names are defined: EBC (essential boundary condition), NBC (natural boundary condition), Temperatures (prescribes temperatures), LINC (linear constraints), JOIN (branch connectivity list), STAGE (computational stage).

TYPE

K string

Type of contribution to the current case. EBC (essential boundary conditions), NBC (natural boundary conditions), Domain.

IDENT

K string

Identifier of contribution. Usually a data set name of the form gname.*.cycle.scycle.case.

SFACTOR

F float

Scale factor. If omitted the default scale factor of 1.0 is assumed.

Access

CASE is created by the input processor and is updated as required by other B2000++ programs, such as the B2000++ solvers.

Validity

Required. B2000++ cannot compute a solution without at least one CASE dataset.

COOR.<br>

The mesh nodes coordinate array (of MemCom dataset type F) contains all node coordinates of a branch, the internal node numbers being implicit: The first row of the array contains the coordinates of internal node 1 (B2000++ database numbering convention!) or node 0 (C++, Python, Simples,), the second row the coordinates of internal node 2(B2000++ database numbering convention!) or node 1 (C++, Python, Simples,), and so on. The external node number of any internal node number is stored in the node parameter list NODA.<br>. The coordinates of an internal node are always formulated in the branch global three-dimensional Cartesian coordinate system.

Content of Dataset

Array of F``e floats with ``NN rows and 3 columns, where NN is the number of nodes in the branch and is equal to size of the array. The point storage scheme assumes values to be stored as follows

x1,y1,z1,x2,y2,z2,...,xn,yn,zn

with x designating the x-coordinate, y the y-coordinate, and z the z-coordinate. Note that coordinates are always stored for all 3 dimensions. The z-coordinate must be set to 0.0 for a 2-dimensional problem!

Access

COOR.br is created by the input processor and it can be modified by any processor.

COOR_IP.<br>.0.0.<cid>

The gradient integration point coordinates table (a MemCom array table of type AT) contains the branch global Cartesian coordinates of all defined integration points. COOR_IP is used together with ELEM_IP.<br>.0.0.<cid>, IP.<br>.0.0.<cid>`, and the sampling-point solution sets to manage the sampling point solution data.

Content of Dataset

Array table with 3 columns containing the 3 global Cartesian coordinates. There are as many rows as there are integration points for the current branch.

Access

Created by the solver processor and it can be modified by any processor.

DOF_INIT.<br>.0.0.<eid>

Specifies the optional initial boundary condition list (a MemCom F array) for a given branch and set identifier <eid> (a positive integer). Initial DOF condition lists will then be activated by an entry in a case definition.

The initial boundary conditions are specified with respect to the reference coordinate system defined by the SYSTEM type (see below).

Content of Dataset Descriptor

Keyword

Type

Description

SYSTEM

K string

Reference coordinate system of the essential boundary conditions described by this set. BRANCH means that the branch coordinate system is reference coordinate system (default). LOCAL means that the node- or element-related local coordinate system is the reference coordinate system (defined as the default reference coordinate system). LOCAL-DEFORMED means that the node- or element-related deformed local coordinate system is the reference coordinate system.

Content of Dataset

Array with a variable number of rows and 3 columns. Column 1 contains the internal node number (B2000++ internal numbering, a positive int starting at 1) or internal element number (a negative int starting at -1) identifier. Column 2 contains the DOF. Note that DOFs are numbered 1,2,3,…. Column 3 contains the boundary condition value.

Access

DOF_INIT is created by the input processor if initial conditions are specified and it is referenced by the CASE.<cid> sets, i.e. CASE.<cid> sets will tell relevant B2000++ processors which initial conditions to include in an analysis.

Validity

DOF_INIT is required whenever initial boundary conditions are present.

DOFD_INIT.<br>.0.0.<eid>

Specifies the optional time derived initial boundary condition list (a MemCom F array) for a given branch and set identifier <eid> (a positive integer). The time derived initial boundary conditions are specified with respect to the reference coordinate system defined by the SYSTEM type (see below).

Content of Dataset Descriptor

Keyword

Type

Description

SYSTEM

K string

Reference coordinate system of the essential boundary conditions described by this set. BRANCH means that the branch coordinate system is reference coordinate system (default). LOCAL means that the node- or element-related local coordinate system is the reference coordinate system (defined as the default reference coordinate system). LOCAL-DEFORMED means that the node- or element-related deformed local coordinate system is the reference coordinate system.

Content of Dataset

Array with a variable number of rows and 3 columns. Column 1 contains the internal node number (B2000++ internal numbering, a positive int starting at 1) or internal element number (a negative int starting at -1) identifier. Column 2 contains the DOF. Note that DOFs are numbered 1,2,3,…. Column 3 contains the boundary condition value.

Access

DOFD_INIT is created by the input processor if time derived initial conditions and it is referenced by the CASE.<cid> sets, i.e. CASE.<cid> sets will tell relevant B2000++ processors which initial conditions to include in an analysis.

Validity

DOFD_INIT is required whenever initial boundary conditions (time derivatives) are present.

DOF solution field

DOF solution field arrays <gname>.<br>.<cycle>.<subcycle>.<cid> contain the problem solution fields for all DOFs at all DOF evaluation points, usually the mesh nodes (a MemCom F array). Any specific DOF is defined by the node type, see NODE-PARAMETERS. The generic dataset name is usually defined in the CASE.<cid> dataset descriptor. Common DOF field generic field names <gname> are DISP (i.e. displacements), FORC (forces), RCFO (reaction forces), or TEMP (temperatures) and HEAT. A summary of the currently defined DOF fields can be found in DOF Fields.

Content of Dataset Descriptor

Keyword

Type

Description

SYSTEM

K string

Reference system. BRANCH (default) or GLOBAL. Usually BRANCH` and``GLOBAL``are equivalent.

TYPE

K string

Type of DOF field. Currently only NODE.

Content of Dataset

Two-dimensional array of F type floats with NN rows and one or more columns (NN is equal to the number or mesh nodes).

Access

The set is created by B2000++ solvers.

EBC.<br>.0.0.<eid>

Essential boundary conditions specify constraints on node (or elements) for a given branch and set identifier <eid> (a MemCom F array) . The essential boundary conditions are described with respect to the domain defined by the DOMAIN type (see below) and they relate to the reference coordinate system defined by the SYSTEM type (see below).

Content of Dataset Descriptor

Keyword

Type

Description

DOMAIN

K string

Type of domain to which the essential boundary conditions described by this set pertain. DOF means degrees of freedom, i.e. the essential boundary conditions are directly related to the computational degrees of freedom. EEDGE means that essential boundary conditions pertain to element edges. EFACE means that essential boundary conditions pertain to element faces. EBODY means that essential boundary conditions pertain to element bodies.

TYPE

K string

Field type of the essential boundary conditions described by this set.``VALUE`` means degrees of freedom.

SYSTEM

K string

Reference coordinate system of the essential boundary conditions described by this set. BRANCH means that the branch coordinate system is reference coordinate system. LOCAL means that the node- or element-related local coordinate system is the reference coordinate system (defined as the default reference coordinate system). LOCAL-DEFORMED means that the node- or element-related deformed local coordinate system is the reference coordinate system.

Content of Dataset

Two-dimensional array of F floats containing as many row as there are boundary conditions. A column contains:

  • Domain type DOF: Column 1 contains the internal node identifier (a positive int value) or element identifier (negative value). Column 2 contains the degree of freedom number. Column 3 and up contain the boundary condition value(s).

  • Domain type EEDGE: Column 1 contains the internal element identifier (a positive int value). Column 2 contains the element local element edge number (see Generic Elements). Columns 3 and up contain the boundary condition values defined by TYPE.

  • Domain type EFACE: Column 1 contains the internal element identifier (a positive int value). Column 2 contains the element local element face number (see Generic Elements). Columns 3 and up contain the boundary condition values defined by TYPE. If the field type is PRESSURE, a single value for a given face is defined, and the a positive pressure acts in the direction of the face normal. For all other field types, all components pertaining to the specific field type are defined (usually 3).

  • Domain type EBODY: Column 1 contains the internal element identifier (a positive int value). Columns 2 and up. contain the boundary condition values defined by the field type TYPE. If the field type is HEAT, a single value for a given DOF is defined. For all other field types, all components pertaining to the specific field type are defined (usually 3).

Node and element identifiers, as well as DOF, element face and edge identifiers must be converted from float to integer!

Node and element identifiers are internal and start with index 1. Edge and face numbers are defined in the Generic Elements section of the user manual.

Access

EBC.<br>.0.0.<eid> is created by the input processor and is updated as required by other processors or control modules.

Validity

EBC.<br>.0.0.<eid> is required whenever essential boundary conditions are present.

ELEMENTSET.<br>.0.0.<name>

The selected elements set array contains a list with element identifiers defined for branch br (a MemCom I array) . name is the set name.

Content of Dataset Descriptor

Keyword

Type

Description

SORTED

I integer

Indicates whether the set is unique and sorted (1) or unsorted (0).

Content of Dataset

Array of I integer values containing internal element identifiers.

Access

Created by the input processor.

element-field

Element fields <gname>.<br>.<cycle>.<subcycle>.<cid> are MemCom F arrays containing element solution values.

Content of Dataset

Two-dimensional array of F type floats with as many rows as there are elements in the branch. Each <gname> field can define one or more columns. A summary of the currently defined element fields can be found in the section Selected Datasets.

Access

Created by the relevant B2000++ solvers.

ELEM_IP.<br>.0.0.<cid>

Element integration point identifiers (MemCom array tables of type AT) contain the branch integration point identifiers for elements. ELEM_IP is used together with COOR_IP, IP, and the sampling-point solution sets to manage the sampling point solution data per load case <cid>.

Content of Dataset

Array table with 2 columns containing the element number and the integration point number. There are as many rows as there are integration points for the current branch.

Access

COOR_IP is created by the solver processor and it can be modified by any processor.

ELEMENT-PARAMETERS

The element parameter table ( a set of MemCom $ tables) specifies the relation between the unique element name and the unique internal element number as well as other element parameters.

Content of Dataset

Array of relational tables, each of them containing the parameters of a given element type:

Keyword

Type

Description

ADD6DOF

I integer

Set to 1 if the element is a candidate to add6dof.

ELNO

I integer

Internal element number of this element. ELNO must be a positive integer.

LTEMP

I integer

Length of temperature array.

NAME

K string

Element name.

NTYPES

I integer

Array containg the node type numbers of all element nodes as defined by NODE-PARAMETERS.

Element Name Conventions

Element name conventions are important for -among others - the baspl++ processor. baspl++ is independent of B2000++ but has a built-in knowledge of the B2000++ element naming conventions and the conventions used to enumerate nodes, edges, element faces, etc.

Element names consist of the generic element name gname followed by attributes, all of them in upper case. The generic name contains several fields separated by dots. The first field describes the element shape and the number of nodes defining the element (see table below).

Shape

Description

C

Solid mechanics cable elements.

R

Solid mechanics rod and cable elements (rods are similar to beams, but they exhibit axial stiffness only).

T

Generic triangular element.

Q

Generic quadrilateral element.

HE

Generic hexahedral element.

TE

Generic tetrahedral element.

PR

Generic prism (‘wedge’) element.

PY

Generic pyramid element.

Access

ELEMENT-PARAMETERS is created by the input processor.

Validity

ELEMENT-PARAMETERS is required.

EDGESET.<br>.0.0.<name>

The selected element edge set array contains a list with element edges defined for branch br (a MemCom I array) . name is the set name.

Content of Dataset Descriptor

Keyword

Type

Description

SORTED

I integer

Indicates whether the set is unique and sorted (1) or unsorted (0).

Content of Dataset

Two-dimensional array of I integer values with NROW rows and 2 columns. NROW is the number of pairs (element_id, edge_id). Column 1 contains the internal element identifier and column 2 the edge number.

Access

Created by the input processor.

EPATCH.<eid>

The MDL mesh patch relational table contains the parameters describing a mesh patch eid (a positive int). The patch will be generated in the input processor, storing the generated nodes, elements and element and node lists on the database.

Note

Use of EPATCH is discouraged.

Content of Dataset

Relational table containing the parameters describing a mesh patch:

Mesh path parameters common to all patch types

Keyword

Type

Description

BRANCH

I integer

Branch number to which patch belongs.

ELEMENT

K string

Element type name.

GEOMETRY

K string

Patch geometry type. PLATE designates a plate with straight edges, CUBE a cube with straight edges, CYLINDER a cylinder.

NE1

I integer

Number of elements in i-direction.

NE2

I integer

Number of elements in J-direction.

NE3

I integer

Number of elements in K-direction.

ORIENTATION

F float

Patch placement in space. Array with 12 elements (3 translations and 3 orientation points). The definition id the same as for node transformations, see TRANSFORMATIONS.

START_ELEMENT_ID

I integer

Start element index of patch element numbering.Element identifiers will be incremented by 1 for each node generated.

START_NODE_ID

I integer

Start node index of patch node numbering. Node identifiers will be incremented by 1 for each element generated.

Geometry-type dependent parameters

Keyword

Type

Description

Px

F float

Definition of a point P1, P2, etc.

THICKNESS

F float

Thickness of patch. Applies to element types requiring specification of thickness.

Others

Geometry-dependent, such as RADIUS, LENGTH, etc.

Additional Information

The following datasets are generated together with EPATCH for a given patch identifier id:

  • EDGESET.<br>.0.0.EPATCH-id-x: List of pairs (element-id, edge-id) for branch br, patch id, and edge x (x=1-12).

  • ELEMENTSET.<br>.0.0.EPATCH-id-B: List of all (element-id) for branch br of patch id.

  • FACESET.<br>.0.0.EPATCH-id-Fx: List of pairs (element-id, face-id) for branch br, patch id, and face x, x taking the values F1..F6.

  • NODESET.<br>.0.0.EPATCH-id-B: List of all (node-id) for branch br, patch id.

  • NODESET.<br>.0.0.EPATCH-id-Ex: List of (node-id) for branch br, patch id, patch edge x, (x=1-12).

  • NODESET.<br>.0.0.EPATCH-id-Fx: List of (node-id) for branch br, patch id, patch face x (x=1-6).

Access

EPATCH.id is created by the input processor.

ETAB.<br>

The element description tables contain all properties of every element of the branch mesh, referring, when required, to other properties, such as property tables or material table. Please refer to the element specific ETAB sections of Chapter Selected Datasets. If, for a specific element, no ETAB section is available, the properties described in this section apply.

Content of Dataset

Sparse table (ST) with as many rows as there are elements in the branch. Each row contains all parameters of the element and is accessed with the same API as the one for MemCom relational tables. Element-type specific data is found in section Element Parameters.

Most common ETAB Element Parameters

Keyword

Type

Description

EID

I integer

External element identifier.

ITYP

I integer

Internal element type identifier, see ELEMENT-PARAMETERS.

MID

I integer

Material identifier. Must be positive or 0. A value of 0 for MID signifies that MID is defined in a PROPERTY table pointed to by PID.

NODES

I integer

Array containing the internal element node indices defining the element, i.e. element connectivity list.

PID

I integer

Property identifier. Must be positive or 0. A value of 0 for PID signifies that PID is not defined for this element, but MID may be defined.

Access

ETAB.br is created by the input processor.

Validity

ETAB.br is required.

FACESET.<br>.0.0.<name>

The selected element face set array contains a list with element faces defined for branch br (a MemCom I array) . name is the set name.

Content of Dataset Descriptor

Keyword

Type

Description

SORTED

I integer

Indicates whether the set is unique and sorted (1) or unsorted (0).

Content of Dataset

Two-dimensional array of I integer integers containing as many rows as there are list entries. Each row list of pairs (elementid, faceid), where elementid is the internal element identifier and faceid the element face number.

Access

Created by the input processor.

FIELDS

The field parameters summary tables (a set of MemCom relational tables) contain the parameters for all defined (solution) fields, such as the generic name of the field, the domain of validity, etc. Fields, such as DOF fields or Sampling Point fields, are generated as a function of the operator and the analysis type, and they contain displacements, temperatures, forces, stresses, etc. While the field parameters are not used by the B2000++ solvers, they are needed by other programs, such as baspl++ post-processor of the b2browser model browser..

Content of Dataset

Array of relational tables, each of the relational tables containing the following field parameters:

FIELD parameters

Keyword

Type

Description

ADDITIVE

K string

Additive field flag. Must be set to YES if the field is an additive field or to NO if the field is not additive.

DISCRETE

K string

Discrete field flag. Must be set to YES if the field is a discrete field or to NO if the field is discontinuous.

GNAME

K string

Generic name of field.

INDEXED

K string

Indexed field flag. Must be set to YES if the field is an indexed field or to NO if the field is an implicitly defined field. If a field is indexed, the first column of the field must contain the external number of the node or element to which the values pertain.

SYSTEM

K string

Coordinate system. Branch means branch-related, GLOBAL means global, LOCAL means (node) local, and LOCAL-DEFORMED means local with respect to the deformed configuration (if any). The default coordinate system must be BRANCH.

TITLE

K string

Short text describing the field (optional).

TYPE

K string

Domain of validity of the field. NODE means values defined at mesh nodes. ENODE means values defined element-wise at the element nodes. CELL or ELEMENT means values defined for elements or cells. FIELD-SAMPLING means “sampling point” field see <gname>.<br>.<cycle>.<subcycle>.<cid> (the standard B2000++ gradient storage scheme).

Access

FIELDS is created empty by the input processor and is updated as required by the programs which generate the specific fields.

Example

A standard deformation analysis DOF field (DISP) for a solid analysis will have the following attributes:

'ADDITIVE': 'NO'
'DISCRETE': 'NO',
'GNAME': 'DISP',
'INDEXED': 'NO',
'TITLE': 'Displacements DX,DY,DZ',
'SYSTEM': BRANCH'
'TYPE': 'NODE'

Note

‘INDEXED’: ‘NO’ mans that the field contains all DOF values for all defined nodes, listed one after the other according to the internal numbering.

‘ADDITIVE’: ‘YES’ means that values across rows can be added (such as forces).

‘DISCRETE’: ‘YES’ means the values are discrete between nodes at which they are defined, i.e. interpolation is not admitted.

IP.<br>.0.0.<cid>`

Stores the gradient integration points natural coordinates (MemCom array tables of type AT) for a given branch and case and is used together with COOR_IP.<br>.0.0.<cid>, ELEM_IP.<br>.0.0.<cid>, and the sampling-point solution sets to manage the sampling point solution data.

Content of Dataset

Array table with 4 columns containing the 3 natural coordinates ()r,s,t) and the layer number. There are as many rows as there are integration points for the current branch.

Access

IP is created by the solver processor and it can be modified by any processor.

JCTS

The branch node connectivity array (a MemCom I array) specifies how branches are interconnected by mesh nodes.

Content of Dataset

I integer array with 6 columns and as many rows as there are coupling conditions. A row contains

BRANCH1, NODE1, DOF1, BRANCH2, NODE2, DOF2

meaning that in the final equations the computational degree of freedom corresponding to internal node NODE1 and degree of freedom DOF1 of external branch BRANCH1 shall be equated to the degree of freedom associated with internal node NODE2 and degree of freedom DOF2 of external branch BRANCH2. If DOF1 is set to 0 the node NODE1, all degrees of freedom of internal node NODE1 will be coupled to internal NODE2, and DOF2 is ignored.

Note that the compound transforms (master-slave transforms) only apply in case the nodes are fully coupled, i.e. if the node NODE1 is set to 0.

Additional Information

Although branch node connectivity lists are most frequently used to link nodes, i.e. to fully couple branches, juncture conditions can require partial compatibility. Hinged joints are a possible application.

Access

JCTS is created by the input processor and it is updated as required by other processors or control modules.

Validity

JCTS is required by the B2000++ solvers whenever more than one branches are present and the branches are explicitly linked with the MDL join command.

LINC[.<eid>]

The linear constraints list (a MemCom I array) contains all linear constraint equations pertaining to a model. A constraint equation is of the form

\[c_1 \cdot u_1 + c_2 \cdot u_2 + .. + c_n \cdot u_n + c_0 = 0\]

where \(c_i\) are real coefficients and \(u_i\) are the degrees of freedom involved. The coefficients \(c_i\) are normalized such that the largest of the coefficients is equal to 1. The constant \(c_0\) can, within reasonable limits, have any magnitude. It is not considered in the search for the largest coefficient.

Content of Dataset Descriptor

Keyword

Type

Description

NEQ

I integer

Number of linear constraint equations.

Content of Dataset

One-dimensional array of F type floats storing the constraint equations one after the other. Each constraint equation is described by

N,WEIGHT,C0,BRANCH1,NODE1,DOF1,C1, ..., BRANCHN,NODEN,DOFN,CN

where N is the number of terms inthe constraint equation, WEIGHT is the weight for the current constraint equation, and C0 the constant \(c_0\). For each coefficient the external branch number BRANCH, the internal node number NODE, the degree of freedom DOF, and the coefficient C must be specified. BRANCH, NODE, and DOF will be used to calculate the global degree of freedom number i for the component \(c_i \cdot u_i\). Thus, the number of floats for describing the equation is 4N+3.

Access

LINC is created by the input processor.

Validity

LINC is required if linear constraint equations are present in a model and if they are required by the LINC option of the CASE.<cid> command.

MATERIAL.<mid>

The element material properties table (MemCom relational table) is a container for storing all parameters of an element material identified by <mid> (a positive int).

Content of Dataset

Relational table describing a specific material. Material property parameters are dependent on the type of material. Specific material are described in the Context-Dependent Datasets section.

Material property keywords

Keyword

Type

Description

SUBTYPE

K string

Descriptive material subtype, such as ISOTROPIC.

TYPE

K string

Descriptive material type, such as SOLID_MECHANICS.

Access

MATERIAL.<mid> is created by the input processor and is accessed by the material classes of B2000++.

MASS_AND_COG.<br>

Mass and volume summary table (a MemCom relational table of type $).

Content of Dataset

Relational table containing the mass and volume of the complete mesh of the branch as well as the element sets.

Access

MASS_AND_COG is created by the b2mass application.

Validity

Optional.

NBC.<br>.0.0.<eid>

A natural boundary condition list (a MemCom F``type array) contains a specific type ``TYPE of natural boundary conditions for a given branch and set identifier <eid> (a positive int). The natural boundary conditions are described with respect to the domain defined by the DOMAIN type (see below) and they relate to the reference coordinate system defined by the SYSTEM type (see below).

Content of Dataset Descriptor

Keyword

Type

Description

DOMAIN

K string

Type of domain to which the natural boundary conditions described by this set pertain. DOF means degrees of freedom, i.e. the natural boundary conditions are directly related to the computational degrees of freedom. EEDGE means that natural boundary conditions pertain to element edges. EFACE means that natural boundary conditions pertain to element faces. EBODY means that natural boundary conditions pertain to element bodies.

TYPE

K string

Field type of the natural boundary conditions described by this set: HEAT means that the natural boundary conditions describe heat sourqces (valid for domain types EEDGE, EFACE, and EBODY)., PRESSURE means that the natural boundary conditions describes a surface pressure., TRACTIONS means that the natural boundary conditions describe the 3 surface traction components in the directions defined by the coordinate system., VALUE means degrees of freedom (domain type DOF).

SYSTEM

K string

Reference coordinate system of the natural boundary conditions described by this set. BRANCH means that the branch coordinate system is reference coordinate system. LOCAL means that the node- or element-related local coordinate system is the reference coordinate system (defined as the default reference coordinate system). LOCAL-DEFORMED means that the node- or element-related deformed local coordinate system is the reference coordinate system.

Content of Dataset

Array of F type floats with as many row as there are noundary condition entries. The number of colums depends on TYPE:

  • Domain type DOF: Column 1 contains the internal node or element identifier. Note that, for the domain type DOF, the element identifier is a negative number to discern it from the node identifier. Column 2 contains either the degree of freedom number (field type VALUE only). Columns 3 and up contain the boundary condition values defined by TYPE. If TYPE is VALUE, only one single value for a given DOF is defined. For all other TYPE types, all components pertaining to the specific TYPE are defined.

  • Domain type EEDGE: Column 1 contains the internal element identifier (positive integer) and column 2 contains the element edge number. The Generic Elements section of the B2000++ Model Description Language User Manual describes the local element edge numbers for all element types. Columns 3 and up contain the boundary condition values defined by TYPE. If TYPE is HEAT, or PRESSURE, only one single value for a given DOF is defined. For all other TYPE types, all components pertaining to the specific field type are defined (usually 3).

  • Domain type EFACE: Column 1 contains the internal element identifier and column 2 contains the element face number. The Generic Elements section of the B2000++ Model Description Language User Manual describes the local element face numbers for all element types. Columns 3 and up contain the boundary condition values defined by TYPE. If TYPE is HEAT, or PRESSURE, only one single value for a given DOF is defined. For all other TYPE types, all components pertaining to the specific field type are defined (usually 3).

  • Domain type EBODY: Column 1 contains the internal element identifier and column 2 and up contain the boundary condition values defined by the TYPE. If TYPE is HEAT, or PRESSURE, only one single value for a given DOF is defined. For all other TYPE types, all components pertaining to the specific field type are defined (usually 3).

Node and element identifiers are internal and start with index 1. Edge and face numbers are defined in the Generic Elements section of the user manual. If the node/elem identifier is positive the identifier is a node. If it is negative, the identifier is an element and the sign must be changed.

Access

NBC.<br>.0.0.<eid> is created by the input processor and is updated as required by other processors or control modules. The NBC sets are referenced by the CASE.<cid> sets.

Validity

NBC.<br>.0.0.<eid> is required whenever natural boundary conditions are present.

NODE-PARAMETERS

The node parameter table (a set of MemCom relational tables) defines the node properties of each node type, such as the type of node or the nodal freedom pattern. The node parameters are defined once during a database creation run, i.e. the initial input processor run. All node parameters must remain constant throughout the computations.

Content of Dataset

Node parameters stored in an array of relational tables. Each table contains the following node property parameters:

Keyword

Type

Description

NAME

K string

Node type name.

NONO

K string

Node type number. Must be greater than 0.

Access

NODE-PARAMETERS is created by the input processor. In the current 4.4 it is created by the function save_node_parameters() in src/b2ip_model.C.

NODESET.<br>.0.0.<name>

The selected nodes set array contains a list of selected nodes of a branch br (a MemCom I``type array). ``name is the set name.

Content of Dataset Descriptor

Keyword

Type

Description

SORTED

I integer

Indicates whether the set is unique and sorted (1) or unsorted (0).

Content of Dataset

Array of I integer integers containing internal node identifiers.

Access

Created by the input processor.

NLCS.<br> Node-local transformations

The node-local transformations arrays contain the node-local rotation matrices (a MemCom F type array). The transformation is defined as

\[u_{nl} = T \cdot u_{bg}\]

where \(u_{nl}\) is a vector formulated with respect to the node-local system and \(u_{bg}\) to the branch global system. The transformation \(T\) contains the 3 normalized base vectors \(e_i\) row-wise. The vectors \(e_i\) are the base vectors of the node-local system with respect to the branch-global system. Node local systems are useful for defining special boundary conditions or for expressing solutions in surface coordinates.

Content of Dataset

Two-dimensional array nlcs[nrows, 9] of F type floats. The number of rows in the set corresponds to the number of node-local systems of the current branch. Each row contains the 3 by 3 rotation matrix stored row-wise. The node attribute table NODA points to the row containing the rotation matrix.

Access

NLCS.br is generated by the input processor: All nodes are scanned for the dofref attribute. If dofref>0 the corresponding transformation is applied and the transformation matrix added to NLCS.br (in ascending internal node order, i.e 0, 1, 2…). Note that other sources than the input processor can produce transformations, i.e dofref is not necessarily at the origin of the node-local transformation matrix of a node!

Validity

NLCS is required if node-local transformations are present, the node-local transformation identifiers stored in the third column of NODA pointing to the corresponding row - 1 of NLCS.

NODA.<br>

The node parameter array (a MemCom I``type array) contains the additional parameters of the nodes defined by the coordinates :ref:`db.COOR` of a branch. Note that the node attributes as well as the node coordinates are defined with respect to the internal continuously numbered node indexes. These must be in the range of 1 to NN``, where NN is equal to the number or rows of COOR.<br>.

Content of Dataset

Two-dimensional array of I integers with NN rows and 4 columns. A row of NODA contains the following attributes:

  • Column 1 contains the external node number of the internal node described by the current row index. Note that B2000++ internal row indexes start with the index 1.

  • Column 2 contains the node-local transformation matrix index i (a positive integer) pointing to the row i of dataset NLCS. A value of 0 means that there is no node-local transformation.

  • Column 3 contains the node-local transformation identifier (a positive integer) as defined by the MDL command transformations and referred to by the dof_ref parameter of the MDL nodes command. A value of 0 means that there is no node-local transformation.

  • Column 4* contains the node type identifier as described by the dataset NODE_PARAMETERS. Note that node type identifiers start with the index 1.

Additional Information

A node i which has a local coordinate system will have an index k>0 in the second column of NODA. The index k then points to the row k of the NLCS.<br> Node-local transformations array (k-1 for C/C++/Python arrays!). Example (C++): Get transformation matrix of node 123:

int i = 123;     // Internal node identifier (numbering starts with 1)
mcInt32 *noda;   // Node attribute array [4*n]. Assumed to be loaded.
mcFloat64 *nlcs  // Local transform array [9*n]. Assumed to be loaded.
mcFLoat64 *tmatrix // Rotation matrix pointer
int k = noda[(i-1)*4 + 1] // Index of local transform (column 2 of noda)
if (k > 0)
    *tmatrix = nlcs[ (k - 1)*9 ] // Transformation matrix

Access

NODA.br is created by the input processor.

Validity

NODA.br is required.

NODE-NORMALS.<br>

The node normals array (a MemCom F type array) contains the list of all node normal vectors of a branch. The node normal vectors must be normalized to 1 and are always formulated in the branch global Cartesian coordinate system. Nodes without normals will have zero values.

Content of Dataset

Array of F type floats with NN rows and 3 columns, where NN is the number of nodes in the branch (NN is equal to the number or rows of COOR.<br>.

Access

NODE-NORMALS.<br> is created by the input processor and can be modified by any processor.

Validity

NODE-NORMALS.br is optional. It is usually present if curved shell structures are defined.

PROPERTY.<pid> Element properties

The element property table (a MemCom relational table) describes property type dependent element parameters referenced by the property identifier <pid>.

Property type BEAM_CONSTANTS

TYPE BEAM_CONSTANTS describes a beam section by all relevant constants. They can be either defined by the cross section constants or by the stiffnesses, which allow for a more general definition, i.e for non-homogeneous materials.

Property type BEAM_CONSTANTS

Keyword

Type

Description

AREA

F float

Cross section area A.

AREA_MOMENTS

F float

Array containing second area moments Jyy, Jzz, Jyz.

BENDING_STIFFNESS

F float

Array containing bending stiffness coefficients E·Jyy, E·Jzz, E·Jyz. If BENDING_STIFFNESS is not specified, AREA_MOMENTS must be specified instead, defining the bending stiffness together with the material identified by MID.

NEUTRAL_AXIS

F float

Array containing section y and z coordinates of neutral axis with respect to the shear center. Default is 0.0 for all values.

MASS

F float

Mass A·density per unit length of beam. If MASS is not specified, AREA has to be specified instead, defining the mass per unit length together with the material identified by MID.

MASS_CENTER

F float

Array containing section y and z coordinates of mass center with respect to the shear center. Default is 0.0 for all values.

MASS_INERTIA_MOMENTS

F float

Array containing mass inertia moments Iyy, Izz, Iyz.

MID

I integer

Material identifier. Required.

NON_STRUCTURAL_MASS

F float

Non-structural mass per unit beam length. Default is 0.0.

NON_STRUCTURAL_MASS_CENTER

F float

Array containing section y and z coordinates of non-structural mass center with respect to the shear center. Default is 0.0 for all values.

SHEAR_CORRECTION_FACTORS

F float

Array containing shear force correction factors Kyy, Kzz, Kyz (array of 3).

SHEAR_STIFFNESS

F float

Array containing shear stiffness A*G*Kyy, A·G·Kzz, A·G·Kyz. If SHEAR_STIFFNESS is not specified, AREA and SHEAR_CORRECTION_FACTORS have to be specified instead, defining the shear stiffness together with the material identified by MID.

TORSIONAL_CONSTANT

F float

Torsional constant Jt (F type float).

TORSIONAL_STIFFNESS

F float

Torsional stiffness Jt·G (F type float). If TORSIONAL_STIFFNESS is not defined TORSIONAL_CONSTANT has to be specified instead, defining the mass per unit length together with the material identified by MID.

TRACTION_STIFFNESS

F float

Axial beam stiffness E*A. If TRACTION_STIFFNESS is not specified, AREA has to be specified instead, defining the traction stiffness together with the material identified by MID.

Property type SECTION

TYPE SECTION describes a beam section by section types according to the MDL manual.

Property type SECTION

Keyword

Type

Description

D1 .. D6

F float

Dimensions of section according to MDL manual.

Iyy, Izz, Iyz

F float

Area moments.

I1, I2

F float

Principal area moments

It

F float

Torsion moment.

yc, zc

F float

Coordinates of centroid.

Inner width of a section (F type float, if applicable).

MID

I integer

Material identifier.

SHAPE

K string

Shape: BAR, BOX, C, I, L, ROD, TUBE.

Property type BEAM_SECTION_MESH

TYPE BEAM_SECTION_MESH describes the beam section by a FE mesh. The preprocessor will then compute all required constants, starting from the mesh and the material.

Property type BEAM_SECTION_MESH

Keyword

Type

Description

MID

I integer

Material identifier.

MODEL

K string

B2000++ MDL input file name describing section mesh and boundary conditions.

Access

PROPERTY.pid is created by the input processor.

Validity

PROPERTY.pid is optional.

<gname>.<br>.<cycle>.<subcycle>.<cid>

A sampling point field (MemCom ST table) contains element gradient fields, such as stress tensors or heat flow vectors. Each element can contain a variable number of sampling points containing one or more float values, usually gradients computed element-wise. The number of sampling point values at any sampling point is constant throughout the whole set. Sampling points are accessed by dataset name and sampling point number.

The field attributes of a sampling points field described by gname are contained in the :ref.`db.FIELDS` dataset.

Sampling point fields are addressed with the internal element identifier starting at 0 and ending at NE-1, where NE is the number of elements in the branch. If a specific element does not have a sampling point field it is up to the application to check.

A summary of the currently defined sampling point fields can be found in the Context-Dependent Datasets section.

Content of Dataset Descriptor

Keyword

Type

Description

COMP_NAMES

K string

Dot-separated string containing the symbolic component names.

DESCR

K string

Short text describing the field, such as “Cauchy stress”, “Green Lagrange strain”.

DOMAIN

K string

Solution field type. Currently set to FIELD-SAMPLING.

JOIN

K string

Reference to ELEM_IP.

LAMBDA

F float

Path parameter. Non-linear static analysis only.

NB_COMP

I integer

Number of components of field.

STAGE_ID

I integer

Computational stage identifier (nonlinear analysis). The stage identifier is identical to the case identifier of the stage as specified in the CASE.<cid> definition.

STAGE

I integer

Internal stage identifier (nonlinear analysis). The internal stage identifier is inserted by the solver and starts with 0 (first stage called in the computation). For each additional stage the value for STAGE is incremented by one.

SYSTEM

K string

Reference coordinate system. BRANCH means that the branch coordinate system is reference coordinate system (default if key is absent). LOCAL means that the node- or element-related local coordinate system is the reference coordinate system (defined as the default reference coordinate system). LOCAL-DEFORMED means that the node- or element-related deformed local coordinate system is the reference coordinate system.

TENSOR_ORDER

I integer

Order of the tensor or -1 if not applicable.

TENSOR_SIZE

I integer

Size of the tensor or -1 if not applicable.

TENSOR_SYM

I integer

Set to 1 if the tensor is symmetric and to 0 if not. If applicable.

TIME

F float

Integration time. Dynamic analysis only.

Content of Dataset

Array table with NE rows, where NE is the number of elements in the branch (equal to the size of dataset ETAB.<br>).

Access

Sampling-point-fields are created by the B2000++ solvers.

Validity

Sampling-point-fields are optional. B2000++ computes sampling points only if the GRADIENT parameter of CASE.<cid> has a non-zero value.

SOLUTION.0.0.0.<case>

The solution summary table (MemCom relational table) contains the global solution attributes of the corresponding case identifier defined by the dataset CASE.<cid>.

Content of Dataset

Relational table containing global solution attributes generated by the solver:

Keyword

Type

Description

ANALYSIS

K string

Effective type of analysis performed for the current case.

DOF_SOL

K string

Generic data set name of the DOF field. Examples: DISP (displacements and optional rotations).

DOFDOT_SOL

K string

Generic data set name of the (optional) time-derived DOF field. Examples: DISPD, TEMPD.

DOFDOTDOT_SOL

K string

Generic data set name of the (optional) twice time-derived DOF field. Examples: DISPDD, TEMPDD.

DRILLS

F float string

“Drill” stiffness weight parameter. field.

GRADIENTS

I integer

Gradients evaluation flag.

LAST_STEP

I integer

Last non-linear load or transient analysis time step.

NBC_SOL

K string

Generic data set name of global natural boundary conditions (“right-hand-sides”). Examples: FORC, HEAT.

NMODES

I integer

Number of (converged) eigenmodes MODE.*.cycle.0.id.mode (if any). Usually defined for free vibration or buckling eigenvalue analysis. Note that the mode’s are numbered 1, 2, 3, …

NSTAGES

I integer

Total number of stages for case id. Defined for non-linear incremental analysis only. For linear analysis NSTAGES is not defined. Note that the stage id’s are numbered 1, 2, 3, …

NSTEPS

I integer

Total number of cycles (steps or increments) for case id. Defined for non-linear incremental analysis only. For linear analysis NSTEPS is not defined. Note that the cycle id’s (steps or increments) are numbered 1, 2, 3, …

RESIDUUM_SOL

K string

Data set name of DOF residua. Examples: RCFO (reaction forces).

SP_SOL

K string

Generic name(s) of sampling point field(s) generated for the current case. If more than one field exists, the field names must be separated by commas. Examples: COOR_IP, DISP_IP,FAILURE_INDEX, FC_TSAI_WU, MBASE_IP, STRAIN, STRESS, VOLUME, HEAT_CAPACITY, HEAT_FLOW.

TERMINATION

K string

Type of termination of solution. NORMAL means termination as required by analysis.

TOL_DYNAMIC

F float

Dynamic analysis error tolerance.

Access

Created by the B2000++ solvers.

Validity

Optional dataset. If absent, B2000++ assumes that the case CASE.id has no solution (relevant for restarts only).

SOLUTION-STAGE.0.0.0.<cid>.<stageid>

The solution stage summary table (MemCom relational table) contains the solution parameters pertaining to all increments of the current analysis for a given solution stage of the case CASE.<cid>. <stageid> is incremented across the stages, starting with 1. Examples of solution parameters are the parameters specified in the MDL case input definition, such as RESIDUE_FUNCTION_TYPE or ANALYSIS, and the ones defined by the solver, such as LAST_STEP.

Content of Dataset

Relational table with solution stage attributes generated by the solver.

Access

Created by the B2000++ solvers.

Validity

Optional dataset. If absent, it is assumed that the case CASE.<cid> has no solution (relevant for restarts only).

SOLUTION-STEP.0.<cycle>.0.<cid>

The solution step table (MemCom relational table) contains the solution parameters produced by the solver for a given solution cycle (or increment or step) of the corresponding case CASE.<cid>. cycle is incremented across the stages, starting with 1.

Content of Dataset

Relational table with the following solution attributes generated by the solver:

Keyword

Type

Description

STAGE_ID

K string

Computational stage identifier. The stage identifier is identical to the case identifier of the stage as specified in the case option of the `stage definition, see CASE.<cid>.

STAGE_ID

I integer

Stage number of the stage pertaining to the solution The stage number is inserted by the solver and starts with 1, i.e. the first or the only stage called in the computation. For each additional stage the value for STAGE_NUMBER is incremented by 1.

TIME

F float

Integration time or control parameter. Note that TIME pertains to static analysis, too, meaning the ‘load factor’!

Access

Created by the B2000++ solvers.

Validity

Optional dataset. If absent, it is assumed that the CASE.<cid> has no solution (relevant for restarts only).

TITLE

The descriptive title (MemCom K array) contains the optional problem title. Any text fields within B2000++ related to TITLE will be set to blank if TITLE is absent.

Content of Dataset

Array of K characters containing a short descriptive text. There is no explicit limitation to the size of the text file, but a title should hold not more than approximately one line of text, i.e around 64 characters.

Access

TITLE is created by the input processor.

Validity

TITLE is optional.

TRANSFORMATIONS

The coordinate systems transformations array (MemCom F array) contains all coordinate system transformations to be applied to points (nodes) and DOFs.

Content of Dataset

Two-dimensional array of F type floats with as many rows as there are defined transformations and with 11 columns. Each row contains:

  • Column 1: External coordinate system definition identifier (a positive integer stored as a float - must be converted to integer).

  • Column 2: Type of coordinate system.

  • Columns 3 to 11: Three points defining the coordinate system (see figures below). Note that the point definitions are with respect to the branch global Cartesian coordinate system.

Additional Information: Transformations

_images/transforms.png

The Cartesian coordinate system transformation is defined as follows: The origin is equal to the point \(P_1\). The local z-axis is defined by \(z = P_2 - P_1\), the local y-axis by \((P_2 - P_2) \times P_3\), and the local x-axis \(x= ((P_2 - P_1) \times P_3) \times (P_2 - P_1)\).

The cylindrical coordinate system transformation is defined as follows: The origin is equal to the point \(P_1\). The cylinder z-axis is defined by \(z = P_2 - P_1\). The tangential (\(\phi\)) direction of a point \(P\) is then defined by \(t = (P -P_1) \times z\) and the cylinder’s radius direction \(r = z \times P_3\). Point \(P_3\), together with \(P_1\) and \(P_2\), spans a plane in which \(\phi=0\), rotating in the positive direction around the local z-axis \(z = P_2 - P_1\). Note: \(_3\) is ignored,i.e. the local \((r,\phi,z)\) system is uniquely defined by the node coordinate \(P\) and points \(P_1\) and \(P_2\).

The spherical coordinate system transformation is defined as follows: The origin is equal to the point \(P_1\). The sphere z-axis is defined by \(z = P_2 - P_1\). The tangential (\(\phi\)) direction of a node \(P\) is then defined by \(t = (`P - P_1) \times z\) and the sphere’s \(\theta\) direction \(r = z \times P_3\). The declination \(\theta\) rotates in a positive direction starting from z. Note: p3 is ignored for transformation, i.e. the local \((\phi,\theta\),z) system is uniquely defined by points \(P_1\) and \(P_2\).

Access

TRANSFORMATIONS is created by the input processor.

Validity

TRANSFORMATIONS is required if coordinate system transformations are specified (see dataset NODA.<br>).

Additional Information: Node transformations

Given the transformation definitions and the coordinates, the input processor computes the effective DOF transformation matrices for all nodes involved. The transformation matrices are stored in data sets NLCS.<br> Node-local transformations and referred to by the second column of the NODA.<br> sets. The transformation is defined as \(u_{nl} = T \cdot u_{bg}\), where \(u_{nl}\) is a vector referring to the node-local system and \(u_{bg}\) to the branch global system. The transformation \(T\) contains the 3 normalized base vectors \(e_i\) row-wise. \(e_i\) defines \(i^{th}\) base vector of the node-local system with respect to the branch-global system:

\[\begin{split}T = \begin{bmatrix} e_{11} & e_{12} & e_{13} \\ e_{21} & e_{22} & e_{23} \\ e_{31} & e_{32} & e_{33} \end{bmatrix}\end{split}\]

VOLUME.<br>

Contains element volumes (MemCom reational table) of all elements of the branch.

Content of Dataset

Array table containing the volume of each element of the branch.

Access

VOLUME is created by the b2mass application.

Validity

Optional.