B2000++ Glossary

DOF

The “Degrees Of Freedom”, i.e the vector of unknowns \(x\) of the problem \(K x = b\), where \(K\) is the global system matrix (“second variation”) and \(r\) the right-hand-side (RHS) vector.

DOF Field

A Node Field containing the “Degrees Of Freedom”. It consists of a rectangular array of nn rows and ndof columns, nn being the number of mesh nodes and ndof the number of DOFs. Examples of DOF fields are displacements in solid mechanics or temperatures in heat conduction problems. The field’s TYPE attribute is NODE and the DOMAIN attribute is DOF (if defined) [1].

NBC Field

An indexed field defining the “natural” boundary conditions, such as forces or heat. The index is either the node or the element identifier. The field’s DOMAIN attribute depends of the domain, as does the TYPE attribute.

Gradients

Gradients (element gradients) are element-wise defined DOF field derivatives and stored in sampling point fields data structures.

EBC Field

An indexed field defining the “essential” boundary conditions, such as “zero constraints”. The index is either the node or the element identifier. The field’s DOMAIN attribute depends of the domain, as does the TYPE attribute.

NODE Field

A field defined at the mesh nodes. It consists of a rectangular array of nn rows and ncol columns, nn being the number of mesh nodes and ncol the number of columns. Examples of node fields are mesh coordinates, displacements in solid mechanics or temperatures in heat conduction problems. The field’s TYPE attribute is NODE and the DOMAIN attribute is DOF (if defined).[#domain]_.

RESIDUUM Field

The RESIDUUM field is \(K x - b\), augmented by the boundary conditions and it is usually defined at the mesh nodes. It consists of a rectangular array of nn rows and ndof columns, nn being the number of mesh nodes and ndof the number of DOFs. Examples of residuum fields are reaction forces RCFO) in solid mechanics or the residual heat (RHEAT) in heat conduction problems.The field’s TYPE attribute is NODE and the DOMAIN attribute is DOF (if defined).[#domain]_.

RHS Field

The RHS “right hand sides” field \(b\) of the problem \(K x = b\). The RHS field is usually defined at the mesh nodes and consists of a rectangular array of nn rows and ndof columns, nn being the number of mesh nodes and ndof the number of DOFs. Examples of right hand side fields are forces in solid mechanics (FORC) or the external heat (HEAT) in heat conduction problems. The field’s TYPE attribute is NODE and the DOMAIN attribute is DOF (if defined).[#domain]_.

SPF Field

The “Sampling Point” field, usually defined element-wise for a given number of sampling points of the same kind [3], such as stresses, strains, element forces and moments, heat flow, heat capacity etc. Sampling points are usually element integration points. A SPF field is stored on the database with the AT (Array Table) data structure [2]. The field’s DOMAIN attribute is FIELD-SAMPLING (the TYPE attribute is not defined).

Footnotes

[1]

The DOMAIN attribute and field attribute can lead to confusion, the reason being historical. Some fields contain the TYPE attribute (‘old style’) and some the DOMAIN attribute.

[2]

The Sampling Point Field storage format consists of a combination of array tables (MemCom AT data type), see Chapter 5 of The MemCom reference manual. Thus, sampling point fields cannot be accessed straightforward. A specific API, such as the Simples SamplingPointField Class class, allows for reading sampling point fields created by the B2000++ solver.

[3]

Unlike DOF fields, element gradients fields cannot be stored in 2-dimensional arrays, because each element type has its own integration (sampling) point scheme and the type of information stored is element dependent. Some elements, such as solid mechanics shell or solid elements usually produce strains and stresses (by default), whereas beam elements produce element forces and moments.