A new solution for topology optimization problems with multiple loads:The guide-weight method

The guide-weight method is introduced to solve two kinds of topology optimization problems with multiple loads in this paper.The guide-weight method and its Lagrange multipliers' solution methods are presented first,and the Lagrange multipliers' soution method of problems with multiple constraints is improved by the dual method.Then the iterative formulas of the guide-weight method for topology optimization problems of minimum compliance and minimum weight are derived and coresponding numerical examples are calculated.The results of the examples exhibits that when the guide-weight method is used to solve topology optimization problems with multiple loads,it works very well with simple iterative formulas,and has fast convergence and good solution.After comparison with the results calculated by the SCP method in Ansys,one can conclude that the guide-weight method is an effective method and it provides a new way for solving topology optimization problems.

TOPOLOGY OPTIMIZATION OF TRUSS STRUCTURES WITH SYSTEMATIC RELIABILITY CONSTRAINTS UNDER MULTIPLE LOADING CASES

In this paper, a mathematical model for topology optimization oftruss structures with constraints of displacement and systemreliability under multiple loading cases is constructed. In order toavoid the difficulty of computing the structure's system reliability,a solving approach is presented in which the failure probability ofsystem is divided into the sum of a all bars' failures probability bymeans of reliability distribution. In addition, by drawing into thereliability safety factor and the fundamen- tal relationship instructural mechanics, all probability constraints of displacement andstress are equiv- alently displayed as conventional form and linearfunction of the design variables.

Exact solution for warping of spatial curved beams in natural coordinates

The purpose of the paper is to present an exact analytical solution of a spatial curved beam under multiple loads based on the existing theory. The transverse shear deformation and torsion-related warping effects are taken into account. By using this solution, a plane curved beam subjected to uniform vertical loads and torsions is analyzed. Accuracy and efficiency of present theory are demonstrated by comparing its numerical results with Heins＇ solution. Furthermore, the effects of the transverse shear deformation and torsion-related warping on deformation of the beam are discussed.

Review of Crashworthiness Studies on Cellular Structures

The application of lightweight structures with excellent energy absorption performance is crucial for enhancing vehicle safety and energy efficiency.Cellular structures,inspired by the characteristics observed in natural organisms,have exhibited exceptional structural utilization in terms of energy absorption compared with traditional structures.In recent years,various innovative cellular structures have been proposed to meet different engineering needs,resulting in significant performance improvements.This paper provides a comprehensive overview of novel cellular structures for energy absorption applications.In particular,it outlines the application forms and design concepts of cellular structures under typical loading conditions in vehicle collisions,including axial loading,oblique loading,bending loading,and blast loading.Cellular structures have evolved to meet the demands of complex loading conditions and diverse research methods,focusing on achieving high-performance characteristics across multiple load cases.Moreover,this review discusses manufacturing techniques and strate-gies for enhancing the manufacturing performance of cellular structures.Finally,current key challenges and future research directions for cellular structures are discussed.The aim of this study is to provide valuable guidelines for researchers and engineers in the development of next-generation lightweight cellular structures.