A finite-element limit analysis for materials with pressure dependent yield behavior

A finite-element limit analysis for materials with pressure dependent yield behavior is presented. An alternative form of the Drucker-Prager yield criterion was applied to model and interpret materials into von Mises materials of inhomogeneous strength. A duality theorem was utilized to convert the lower bound formulation to the upper bound formulation. A penalty method was used to transform the constrained optimization problem to an unconstrained one. A finite-element method was then employed to discretize the unconstrained optimization problem into a finite-dimensional one. Finally, a combined smoothing and successive approximation (CSSA) algorithm was applied to solve the unconstrained optimization problem. Namely, a fixed-point theorem and Gaussian elimination were used to solve and update the algebraic equations iteratively.; The finite-element limit analysis was verified rigorously and thoroughly by comparing numerical results with exact closed form solutions. Good agreement was obtained in terms of limit load factors and failure mechanisms. Its versatility and effectiveness were then demonstrated by solving practical plasticity problems in geotechnical engineering. The practical examples included bearing capacity problems, slope stability problems, and tunnel stability problems. A computer code, with a built-in mesh generation function, was developed to perform the numerical examples. The corresponding failure mechanisms and motion of failure zones were shown explicitly.