| Isogeometric analysis(IGA)is a new numerical method that combines traditional CAE and CAD in the field of computational mechanics,and successfully solves the disconnection between the analysis and geometric models of the finite element method,poor continuity between elements,and higher-order element efficiency.Low-level defects provide engineering designers with high-precision,high-efficiency,and high-performance calculation methods in the field of topology optimization.In addition,with the application of topology optimization theory in actual engineering structures,not only the accuracy of the calculation method should be improved,but also the accuracy of the model itself should be improved.In practical situations,the properties of various points in the material cannot be the same everywhere,so the simple model can no longer meet the high accuracy requirements proposed in the engineering practice.At present,isogeometric topology optimization of granular material structures is one of the most challenging topics in the field of structural optimization design,which is of great significance for solving practical engineering problems.This article uses adaptive granular micromechanics approach,directly from the microscopic behavior of particle-pair interactions under given strain conditions,to simulate the macroscopic behavior of the material,so as to obtain the constitutive relationship of each material point.With minimum compliance as the objective function,isogeometric topology optimization model based on the constitutive relationship of granular materials is established,the calculation accuracy of isogeometric analysis is analyzed,and the influence of isogeometric analysis and finite element analysis on the results of topology optimization is studied,the tensile and compression asymmetry of isogeometric topology optimization based on the constitutive relationship of granular materials under different tensile-compression stiffness ratios is discussed.In Matlab software platform,isogeometric analysis is used to write isogeometric topology optimization program such as a continuum structure based on the constitutive relationship of granular materials.Main research topics are listed as following:1.To study the accuracy of isogeometric analysis in two-dimensional linear elasticity problems,the element displacement cloud diagram and stress cloud diagram are given,and the calculation errors of isogeometric analysis and analytical solution in displacement and stress are analyzed.It replaces the traditional finite element analysis with isogeometric analysis in topology optimization,and discusses the computational advantages of isogeometric analysis in topology optimization.2.Establish isogeometric topology optimization model based on the two-dimensional continuum structure using the constitutive relationship based on granular micromechanics.Isogeometric analysis was used to solve the structure’s principal stress magnitude and direction,and the tension and compression state of the material points were judged according to the positive and negative principal stresses.Considering the typical rectangular and curve domain structure optimization models,the finite element analysis and isogeometric analysis were compared for granular materials.The influence of the topological configuration of the continuum structure is analyzed on the tension and compression area of the two-dimensional topological structure under different tension-compression stiffness ratios.3.Using the 3D evolutionary structural optimization,isogeometric topology optimization model of continuum structure based on the 3D granular micromechanics constitutive relationship is established.The effects of a given tension-compression stiffness ratio and volume constraint on the topological configuration of a three-dimensional continuum structure are studied.The validity of the optimization method is verified by threedimensional numerical examples of a single-load cantilever structure,a multi-load cantilever structure and a square stool structure. |
