Finite element analysis of limit load and localized failure of structures

摘要

The dissertation deals with limit load and limit ductility analysis of structures by the finite element method. When structure is at its limit load, several structural components behave inelastically, while in the critical parts of the structure, due to localization of inelastic strains, failure of material appears. Localized effects in brittle materials are related to appearance and formation of a large (macro) crack, while failure in ductile materials is governed by localized shear bands. The study of limit load is thus related to modeling both standard inelastic ma- terial effects, as well as modeling of localized failure of material, often reffered to as material softening. Standard inelastic material effects are in this work described with elastoplastic, elas- toviscoplastic and nonlinear elastic material models. All the material models are defined at the level of stress-resultants. Several mathematical approaches and numerical algorithms for modeling localized effects are at hand, but they are often inefficient or inaccurate. Therefor, we use an up-to-date approach, based on a finite element method with embedded discontinuity. We derive new finite element formulations with a quite complex kinematics of the basic elements, as well as rather complex description of discontinuous displacement fields. We derived several finite element formulations for analysis of different structural components. First we present a finite element for limit load analysis of reinforced concrete plates. Stress-resultant elastoplas- tic and elastoviscoplastic plate finite element formulation along with a unified computational procedure that covers both formulations are presented next. Further, a nonlinear shell finite ele- ment, based on a two-surface yield function, that includes both isotropic and kinematic material hardening is presented. The last two finite elements derived in this work are intended to model the localized failure in planar beams and 2D solids. The embedded discontinuity in rotations was built into elastoplastic Euler-Bernoulli beam finite element, and a procedure, based on a precomputed analysis of a part of a structure, by using a refined numerical model, is proposed to obtain the beam constitutive model parameters. Finally, we derive an elastoplastic quadri- lateral two-dimensional finite element formulation with embedded strong discontinuity, whose kinematics can model linear jumps in both normal and tangential displacements along the dis- continuity line. Numerical simulations show, that the derived finite elements, along with the accompanied numerical algorithms, are an efficient and a rather robust tool for limit load and failure analysis of structures. Among other examples, we present a simulation of crack growth in brittle material and a simulation of shear band failure in ductile material. All the computer codes of the finite element formulations presented in this work have been generated through the symbolic programming of the finite element computer code and the expression optimization in AceGen computer program. The performance of these elements has been presented in numerous numerical examples, all performed by the AceFem computer program.