Optimization of the initial post-buckling response of trusses and frames by an asymptotic approach

2025-05-14

AI Summary

This work addresses the optimization of initial post-buckling response and defect sensitivity in truss and frame structures. We propose a novel methodology integrating asymptotic post-buckling theory with structural optimization. Specifically, the first- and second-order asymptotic coefficients—governing post-buckling slope and curvature, respectively—are explicitly incorporated as design objectives, enabling direct control over nonlinear response morphology within simultaneous size and topology optimization for the first time. A nonlinear surrogate modeling strategy—combining end compliance and complementary energy minimization—is employed to efficiently capture geometric nonlinearity. Across multiple benchmark examples, the approach concurrently minimizes both linear and nonlinear compliance while substantially enhancing robustness against geometric imperfections. Numerical results demonstrate high accuracy and computational efficiency. The framework provides a scalable theoretical foundation and practical tool for post-buckling-constrained structural optimization.

Technology Category

• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Asymptotic post-buckling theory is applied to sizing and topology optimization of trusses and frames, exploring its potential and current computational difficulties. We show that a designs' post-buckling response can be controlled by including the lowest two asymptotic coefficients, representing the initial post-buckling slope and curvature, in the optimization formulation. This also reduces the imperfection sensitivity of the optimized design. The asymptotic expansion can further be used to approximate the structural nonlinear response, and then to optimize for a given measure of the nonlinear mechanical performance such as, for example, end-compliance or complementary work. Examples of linear and nonlinear compliance minimization of trusses and frames show the effective use of the asymptotic method for including post-buckling constraints in structural optimization.

Problem

• Optimize truss frame post-buckling response asymptotically
• Control designs' post-buckling slope curvature coefficients
• Reduce imperfection sensitivity nonlinear performance optimization

Innovation

• Asymptotic post-buckling theory optimizes trusses and frames
• Controls post-buckling response with two asymptotic coefficients
• Approximates nonlinear response for performance optimization