Novel Numerical Procedures for Limit Analysis Implementation to Planar Axisymmetric and Three Dimensional Geomechanics Stability Problems

Abstract

The Current research in the field of computational limit analysis dwells upon the development of numerical tools which are sufficiently efficient and robust to be used in engineering practices. This places demands on the numerical discretization strategies adopted as well as on the mathematical programming tools used to solve the associated optimization problems, which are the key ingredients of a typical computational limit analysis procedure. The traditional FEM based discretization is subjected to various issues, like: (i) volumetric locking, (ii) high sensitivity to mesh geometry, and (iii) difficulty in mesh generation and remeshing of higher order and 3D elements. Moreover, the optimization problem associated with limit analysis is nonlinear, non-smooth and sparse in nature. The linear and nonlinear programming are not so efficient in solving these type of problems. The three major objectives of present research work are (i) to improve the accuracy and efficiency of limit analysis solutions by using advanced spatial discretization techniques, (ii) to express the optimization problems associated with computational limit analysis as conic programming problem, so that it can be solved efficiently using primal-dual interior point method, and (iii) to solve complex planar, axisymmetric and three-dimensional geomechanics problems using developed numerical techniques...