Because of descriptive nonlinearity and computational inefficiency,topology optimization with fatigue life under aperiodic loads has developed slowly.A fatigue constraint topology optimization method based on bidirect...Because of descriptive nonlinearity and computational inefficiency,topology optimization with fatigue life under aperiodic loads has developed slowly.A fatigue constraint topology optimization method based on bidirectional evolutionary structural optimization(BESO)under an aperiodic load is proposed in this paper.In viewof the severe nonlinearity of fatigue damagewith respect to design variables,effective stress cycles are extracted through transient dynamic analysis.Based on the Miner cumulative damage theory and life requirements,a fatigue constraint is first quantified and then transformed into a stress problem.Then,a normalized termination criterion is proposed by approximatemaximum stress measured by global stress using a P-normaggregation function.Finally,optimization examples show that the proposed algorithm can not only meet the requirements of fatigue life but also obtain a reasonable configuration.展开更多
The mechanism of three⁃order Rubiks Cube(RC)has the characteristics of recombination and variable degree of freedom,and it is difficult to accurately describe the degree of its freedom.This paper takes RC as...The mechanism of three⁃order Rubiks Cube(RC)has the characteristics of recombination and variable degree of freedom,and it is difficult to accurately describe the degree of its freedom.This paper takes RC as the research object,and the adjacency matrix is constructed based on topology and graph theory in order to describe the variation rule of topological configuration in the single layer rotation of RC.In this paper,the degree of freedom of the RC in any shape can be described by defining the concept of entanglement degree of freedom,establishing a set of adjacency matrix,and determining the degree of freedom of the RC which is attributed to the number of non⁃zero elements in the set of adjacent matrix.The prime number is proposed to describe the rotation of the RC combined with the rotation recognition of RC,which is simple and convenient for computer processing.The research contents in this paper are beneficial to the study of RC from the perspective of mechanism science.Meanwhile,it is of great significance to the study of other complex mechanisms with variable degrees of freedom.展开更多
基金Chinese National Natural Science Foundation(No.51890881)Science and Technology Project of Hebei Education Department(Nos.ZD2020156,QN2018228).
文摘Because of descriptive nonlinearity and computational inefficiency,topology optimization with fatigue life under aperiodic loads has developed slowly.A fatigue constraint topology optimization method based on bidirectional evolutionary structural optimization(BESO)under an aperiodic load is proposed in this paper.In viewof the severe nonlinearity of fatigue damagewith respect to design variables,effective stress cycles are extracted through transient dynamic analysis.Based on the Miner cumulative damage theory and life requirements,a fatigue constraint is first quantified and then transformed into a stress problem.Then,a normalized termination criterion is proposed by approximatemaximum stress measured by global stress using a P-normaggregation function.Finally,optimization examples show that the proposed algorithm can not only meet the requirements of fatigue life but also obtain a reasonable configuration.
基金the National Natural Science Foundation of China(Grant No.51775473)the Natural Science Foundation of Hebei Province(Grant No.E2018203140).
文摘The mechanism of three⁃order Rubiks Cube(RC)has the characteristics of recombination and variable degree of freedom,and it is difficult to accurately describe the degree of its freedom.This paper takes RC as the research object,and the adjacency matrix is constructed based on topology and graph theory in order to describe the variation rule of topological configuration in the single layer rotation of RC.In this paper,the degree of freedom of the RC in any shape can be described by defining the concept of entanglement degree of freedom,establishing a set of adjacency matrix,and determining the degree of freedom of the RC which is attributed to the number of non⁃zero elements in the set of adjacent matrix.The prime number is proposed to describe the rotation of the RC combined with the rotation recognition of RC,which is simple and convenient for computer processing.The research contents in this paper are beneficial to the study of RC from the perspective of mechanism science.Meanwhile,it is of great significance to the study of other complex mechanisms with variable degrees of freedom.
