Rod/cable Elements for Stress Analysis

1. Introduction

The rod/cable elements are designed for static and dynamic, linear and nonlinear analysis of truss and cable structures. They are elastic in axial direction and as such depend on the displacement degrees-of-freedom at the nodes. The Total-Lagrangian approach is employed to allow for arbitrary rigid-body motions.

Rod/cable elements may contain an initial strain, stress, or force.

2. Element Types

The following element types are available:

Table 14. Rod/Cable Elements for Stress Analysis

Element type Remarks
R2.S A two-node, fully-integrated linear rod/cable element. The shape functions are compatible with the B2.S.RS beam element and with the element edges of linear shell and continuum elements.
R3.S A three-node, fully-integrated quadratic rod/cable element. The shape functions are compatible with the B3.S.RS beam element and with the element edges of quadratic shell and continuum elements.
R4.S A four-node, fully-integrated cubic rod/cable element. The shape functions are compatible with the B4.S beam element and with the element edges of cubic shell and continuum elements.


3. Required element attributes

mid m

Specifies the element material number m. The elements can process materials of the following types:

The same definition will be used for all elements defined hereafter, until a new mid option is encountered or until the eltype command is specified.

area t

Specifies the cross section area t. The same definition will be used for all elements defined hereafter, until a new area option is encountered or until the eltype command is specified.

4. Optional element attributes

initial_strain_xx exx

Defines an initial strain exx. The initial strain is constant over the section and along the element x-axis. The same definition will be used for all elements defined hereafter, until a new initial_strain_xx option is encountered or until the eltype command is specified.

initial_stress_xx sxx

Defines an initial stress sxx. The initial stress is constant over the section and along the element x-axis. The same definition will be used for all elements defined hereafter, until a new initial_stress_xx option is encountered or until the eltype command is specified.

initial_force_x fx

Defines an initial force fx acting at the centroid of the section. The initial force is assumed constant along the element x-axis. The same definition will be used for all elements defined hereafter, until a new initial_force_x option is encountered or until the eltype command is specified.

initial_force_off_x fx my mz

Defines an initial force fx and an initial moment my (around the local y-axis) and an initial moment mz (around the local z-axis) acting at the centroid of the section. The initial force and the moments are assumed constant along the element x-axis. The same definition will be used for all elements defined hereafter, until a new initial_force_off_x option is encountered or until the eltype command is specified.

group eid

Defines the element group number gid (a non-negative integer number). The default group number is 0. The same definition will be used for all elements defined hereafter, until a new group option is encountered or until the eltype command is specified.

non_structural_mass v

Defines the non-structural mass per unit length. Default is 0. The same definition will be used for all elements defined hereafter, until a new non_structural_mass option is encountered or until the eltype command is specified.

5. Stresses and Strains

Axial stresses, strains, and forces stored on database are all expressed in the element-local coordinate system. For nonlinear analysis, the strain is the Green-Lagrange strain, while the stress is the Cauchy stress.

Axial stresses are stored in the SECTION_STRESSES dataset/baspl++ Field. Axial strains are stored in the SECTION_STRAINS dataset/baspl++ Field. Axial section forces are stored in the ELEMENT_FORCES dataset/baspl++ Field.