A Fast First-Order Optimization Approach to Elastoplastic Analysis of Skeletal Structures

TL;DR

This paper introduces an accelerated proximal gradient method for large-scale elastoplastic analysis of skeletal structures, reformulating the problem as an unconstrained nonsmooth convex optimization to improve computational efficiency.

Contribution

It presents a novel formulation of elastoplastic analysis as an unconstrained nonsmooth convex problem and applies an accelerated gradient method for faster solutions.

Findings

Effective for large-scale elastoplastic analysis

Accelerated method outperforms traditional approaches

Warm-start strategy speeds up incremental analysis

Abstract

It is classical that, when the small deformation is assumed, the incremental analysis problem of an elastoplastic structure with a piecewise-linear yield condition and a linear strain hardening model can be formulated as a convex quadratic programming problem. Alternatively, this paper presents a different formulation, an unconstrained nonsmooth convex optimization problem, and proposes to solve it with an accelerated gradient-like method. Specifically, we adopt an accelerated proximal gradient method, that has been developed for a regularized least squares problem. Numerical experiments show that the presented algorithm is effective for large-scale elastoplastic analysis. Also, a simple warm-start strategy can speed up the algorithm when the path-dependent incremental analysis is carried out.