Isogeomtric Analysis Method And Their Application In Structural Mechanics Analysis And Shape Optimization Design

Isogeometric analysis(IGA)method based on spline theory is a new numerical computation method,which is proposed by Professor Hughes of United States from the perspective of a unified CAD and CAE,in order to achieve the seamless integration between CAD and CAE.The core idea of IGA is to use the non-uniform rational B-spline(NURBS)basis functions for analysis as is used to build accurate geometry.It can avoid loss of exact geometric information in conventional finite element method(FEM)due to using approximate grids,which greatly improves accuracy of the gradient field of variables.The spline function can be very convenient for geometry refinement under keeping the geometry unchanged.By reading a large number of Chinese and English papers,this paper mainly studies the IGA algorithm based on NURBS and Bézier extraction of NURBS and their Application in structural mechanics analysis and shape optimization design.The analysis of the traditional finite element CAD and CAE can not be seamless integration,so the background,characteristics and research status of IGA are introduced.Basic theory of B-spline and NURBS in IGA are introduced and the refinement technique of NURBS is explained by relevant examples.From the isoparametric finite element principle,the analysis theory of IGA is deduced which involves the application of the Gaussian integration and the discussion of unit control point index.According to the principle of IGA,the timoshenko problem is used as a numerical example to validate the isogeometric code for 2D probelem by comparing the isogeometric solution with the analytical and the finite element solution.Then the method is applied to two-dimensional open spanner and three-dimensional solid shell.IGA algorithm based on Bézier extraction of NURBS is studied,which contains Bézier decomposition and Bézier extraction operator.A one-dimensional poisson problem is used as a numerical example to validate the Isogeometric analysis algorithm based on Bézier extraction of NURBS.Then the method is applied to a quarter of a circular disk,trapezoid plate and infinite plate with hole which is in comparison with the result of different analysis methods.Finally,timoshenko beam,trapezoid plate and open spanner are optimized by the a particle swarm optimization algorithm with weight mechanism and analyzed by IGA.