استفاده از روش هاي بدون شبكه در تعيين توپولوژي بهينه سازه ها

چكيده انگليسي :

99 Structural Topology Optimization Using Mesh free Methods Nafiseh Niknejadi nafiseh niknejad@yahoo com Date of Submission March 3 2012 Department of Civil Engineering Isfahan University of Technology Isfahan 84156 83111 IranDegree M Sc Language FarsiSupervisor Dr Bijan Boroomand boromand@cc iut ac ir Advisor Dr Mojtaba Azhari Mojtaba@cc iut ac ir AbstractBeing one of the most challenging tasks in structural designs topology optimization seeks a suitable layoutof structures for the required structural performance In this regard various techniques and methods havebeen developed during the past decade The choice of theory and methodology of the structural analysisplays a crucial role in the design Recently a number of mesh free methods have been proposed to alleviatesome drawbacks of mesh based approaches In this dissertation the procedure of topology optimization of continuum structures is combined with somemesh free approaches In this regard at first a mesh free method known as Generalized Finite Point Method GFPM is used to perform structural response analysis as well as the sensitivity analysis This methodemploys a weighted residual approach and is based on a sub domain collocation technique The shapefunctions are constructed by the weighted least square WLS and the system of algebraic equations isconstructed by the use of weak form of the generic governing equation of elasticity problem Due to the useof weak form of equations the method can consider density variation which is an important requirement intopology optimization but the results show that GFPM does not perform accurate sensitivity analysis whenused in optimization algorithm To improve the method and eliminate some instability effects two newmesh less methods have been proposed and employed in topology optimization procedure which are called Petrov Galerkin Free Patch Method and Free Patch Method These methods are based on employingfinite element shape functions as basis functions to approximate displacement field and using the weak formof the governing equations Unlike the other integral based mesh free methods the computation of therelated integrals is significantly simple and cheap so the proposed methods will save the time and cost ofanalysis A density approach is employed to find the optimal material distribution in a continuum domain The densityat a generic point is evaluated by interpolation between a set of nodal values which are independent fromthose used for the analysis To interpolate the density value from nodal quantities a set of linear hat shapefunctions are defined over elements that have been used for discritization of the material field To obtain theoptimum configuration a restriction method is employed which is based on a sequential mesh refinementstrategy during the optimization procedure Moreover The optimization problem is solved by using theMethod of Moving Asymptotes MMA where the objective function is the compliance energy and nodaldensities are used as design variables The solutions of several 2D structural optimization problems with various boundary conditions are presentedto validate the accuracy efficiency and applicability of the proposed methods It has been observed that thepresented methods prevent some numerical instabilities such as appearance of checkerboard patterns andmesh dependence phenomena Key words Topology Optimization Mesh free Methods Numerical Instability

نيك نژادي، نفيسه

استفاده از روش هاي بدون شبكه در تعيين توپولوژي بهينه سازه ها

بهينه سازي توپولوژي , پالايش متوالي شبكه