Sequential elastic adaptive NS-FE analyses for lower-bound limit load determination of plane-strain structures

Abstract

The paper proposes the sequential elastic analyses run within the node-based smoothed finite element (NS-FE) framework incorporating an automatic adaptive mesh scheme to converge the lower-bound collapse load limit of plane-strain structures. The approach is familiar to practical designers as it solely involves a series of linear elastic analysis solves. Each of which performs a modified version of elastic compensation method that appropriately considers the modulus variations of some critical members. The nonlinear constitutive formulations describing intrinsic material properties can be directly accommodated. The NS-FE method simply adopts the low-order displacement functions, whilst the mesh adaptive algorithm employs the newest-bisection criteria with the novel modulus variation error indicators. A number of numerical examples and benchmarks involving the plane-strain structures with vertex and curve geometries illustrate the accuracy and efficiency of the proposed method. The approach overcomes the challenges associated with stress singularity and volumetric locking phenomena in an incompressibility condition. The collapse load solution converges to the lower-bound limit at modest computing efforts, where the final NS-FE layout (namely fine meshes over the areas developing high modulus variation rates and at the same time coarse meshes for those undergoing elasticity) depicts the failure lines of structures and hence mechanisms.