Data-driven FEM cluster-based basis reduction method for ultimate load-bearing capacity prediction of structures under variable loads

Abstract

The structural ultimate load-bearing capacity plays an influential role in engineering applications. Melan’s static shakedown theorem offers a valuable approach for predicting the lower bound of shakedown loading factors and providing a safer shakedown domain when the structures are subjected to cyclic variable loads. However, the associated nonlinear mathematical programming is plagued by substantial computational expenses due to excessive design variables and constraints. Inspired by the data-driven FEM Cluster-based Analysis (FCA) [44], [45], [46], [47] for predicting nonlinear effective properties of RVE of heterogeneous materials very efficiently, this paper introduces a novel FEM cluster-based basis reduction method to predict the shakedown domain of structures. Firstly, the FEM elements of discretized structures are grouped into several clusters using the elastic strain tensor under different load vertex cases, which differs from the orthogonal loading conditions for clustering RVE. In this way, similar mechanical behavior in each cluster of the structures is expected in future loading. Then, the cluster eigenstrain-driven algorithm is employed to construct the self-equilibrium stress (SES) basis vectors, which should satisfy the equilibrium equation and statical boundary condition. Furthermore, the essential time-independent beneficial residual stress in the static shakedown analysis is represented as a linear combination of the constructed SES basis vectors based on the basis reduction method, which can reduce a large number of time-independent residual stress to several linear combination coefficients. In addition, the reduced-order model (ROM) is constructed by the cluster SES, which are volume averaged stresses of the element SES basis vectors within each cluster. Based on the ROM, a constraint reduction strategy (CRS) is introduced to selectively remove stress constraints significantly below yield stress from the enormous element-wise yield constraint set. These innovations decrease the number of design variables and nonlinear constraints in the shakedown optimization, thus significantly enhancing computational efficiency. Several numerical examples illustrate the effectiveness and efficiency of the proposed shakedown analysis method of FCA.