Elasto-Plastic Large Displacement Analysis Of Spatial Skeletal Structures

In recent decades, the geometrical and material nonlinear analysis of spatialskeletal structures has captured the interest of many researchers. The key point of thisproblem is how the plastic deformation is considered in structural large deformation.Until now, some methods have been proposed, but each has its own drawbacks. Thisthesis conducts research on the elasto-plastic large displacement analysis of spatialskeletal structures. Based on the beam theory, this thesis analyzes the elasto-plasticbehavior of the beam ends’ cross-section and derives the element’s elasto-plastic tangentstiffness matrix.The widely used cylindrical arc-length method is adopted for the continuation ofthe solution path and is reviewed. A line search method is introduced to accelerate theconvergence speed. Based on the finite element method of beam, the tangent stiffnessmatrix of the beam element is presented and verified by several numerical examples.The above two work lay the foundation for the elasto-plastic analysis of the spatialskeletal structures.In order to reduce the computation amount of the elasto-plastic analysisappropriately, the plastic deformation is assumed concentrated on both ends of theelement while the inner part keeps elastic. The end cross-sections of the element arethen discretized into several small areas. The elasto-plastic behavior of each small areais analyzed to form the elasto-plastic stiffness of end cross-section. The element’selasto-plastic tangent stiffness is obtained from integration of cross-section stiffnessesalong the member by using Gauss-Lobatto quadrature scheme. Based on theincremental finite element method of material nonlinearity, the incremental constitutiverelationship of the small areas is set up which includes the isotropic hardening ofmaterial. Besides, the loading and unloading cases are distinguished in detail and aneffective algorithm is presented to correct the stresses which drift from the yield surfaceduring material nonlinear analysis.In view of the difference between the truss element and beam element, theelasto-plastic tangent stiffness of the truss element is derived. A force recoveryprocedure for the truss element is introduced based on the return mapping algorithm.Numerical examples show that this truss model can be applied to reticulated shells with plenty of rods.Based on above theory, a geometrical and material nonlinear analysis program forspatial structures is coded by using Fortran95. This program can search the full range ofload-displacement curve effectively. Several numerical examples are analyzed by thisprogram, the results of which are compared with those obtained from ABAQUS andANSYS which verifies the accuracy and reliability of the proposed approach.