Substructure preload history

This problem contains basic test cases for one or more Abaqus elements and features.

This page discusses:

ProductsAbaqus/Standard

Effects on element and nodal output variables

Elements tested

T2D2

Features tested

Preloading of a substructure followed by perturbation and general steps and the recovery of nodal and element variables.

Problem description

A substructure is formed from a one-element truss model constructed of an elastic-plastic material. The substructure will be subjected to a preload (axial force) that causes inelastic strains. The substructure stiffness matrix is then formed about this base state. Additional loads are applied during global usage through a perturbation step and a general step.

Results and discussion

STEPLOADS11E11EE11PEEQ
Preload Δ⁢u=.0015 32721 1.499E−3 1.0907E−3 4.082E−4
Perturbation 1000 1003 3.342E−5 3.342E−5 n/a
General 1000 1003 3.342E−5 3.342E−5 4.082E−6

The results from the global analysis are consistent with the assumptions of substructures. Namely, the elastic stiffness is used during substructure generation, and initial stress stiffening effects are considered. The stresses and strains from both steps are in addition to the values from the preload step.

Effects of nonlinearities on the stiffness matrix

Elements tested

T2D2

Features tested

Effects of material and geometric nonlinearities on the resulting stiffness matrix of a substructure.

Problem description

Two substructures are created from single-element truss models, one made of a pure elastic material and the other made of an elastic-plastic material. Young's modulus is 3.0E5 in both models, and both structures are subject to a preload (prescribed displacement). The effects of the nonlinearities are incorporated into the static analysis by using the NLGEOM parameter. The magnitude of the applied load is high enough to ensure plastic deformation in the elastic-plastic material. The tangent stiffness value, k11, obtained for each case is compared to the corresponding value obtained by the analysis of an analogous global model without substructures.

Results and discussion

 SubstructureNo substructure
NLGEOMNO NLGEOMNLGEOMNO NLGEOM
Pure elastic 2.243E5 3.000E5 2.243E5 3.000E5
Elastic-plastic 2.403E5 3.000E5 2.403E5 3.000E5

For the substructure models analyzed without the NLGEOM parameter, the substructure stiffness is the elastic stiffness itself, and material nonlinearities such as plasticity are not accounted for during the creation of the substructure. However, when NLGEOM is used in the preload history definition, the effects of stress stiffening and material nonlinearity are accounted for.

Effects of contact constraints on the stiffness matrix

Elements tested

CPE4

Features tested

Effects of contact constraints on the resulting stiffness matrix of a substructure.

Problem description

A substructure is formed from a one-element model constructed of an elastic material. A rigid surface consisting of R2D2 elements is moved down to compress the element in the first step. In the second step the element is moved across the rigid surface to generate frictional forces at the contact interface. The substructure stiffness matrix is then formed about this base state. Additional loads are applied during global usage through a perturbation step.

Results and discussion

The results from the global analysis are consistent with the assumptions of substructures; i.e., the nodes on the secondary surface that are in contact prior to the generation of the substructure stiffness matrix are tied to the main surface. The stresses and strains are in addition to the values obtained from the preload steps.