The Research Of Fast CAD/CAE Intergrated Mechanical Structural Design And Uncertainty Analysis Based On Isogeometric Analysis

Numerical simulation has become an indispensable tool in engineering design,analysis and/or optimization,as well as having been widely applied in automobile,ship,aerospace,civil engineering and other fields.However,limited by the huge gap between CAD and CAE existed in traditional numerical simulation and the large amount of time consumed by repeatedly evaluation of modified structure,it is difficult to realize the designers/engineers' dream that conveniently,quickly and exactly represent and modify the CAD geometric model,as well as obtaining the CAE analysis results as soon as possible,even in real time,hence promote and accelerate the product development and improve the social benefits.Moreover,although the Tailor Rolled Blank(TRB)has been widely concerned,there is no general or even rough rule that can accurately represent and continuously optimize the thickness of the TRB.In addition,considering the uncertain situation widely exists in system,and the inherent uncertainty of the system may have a significant influence on the behavior of structure.Consequently,the traditional analysis method based on the determined parameters cannot get a correct or optimal results.Therefore,this paper tries to solve the problems mentioned above,proposing the rapid integration of CAD/CAE based structural design and optimization,and the uncertainty analysis framework.The research mainly includes the following aspects:Firstly.it is the first time that the isogeometric independent coefficient(IG A-IC)method is proposed for the real-time CAD and CAE integration for structural local shape and material modifications.First,we seamlessly integrate CAD and CAE based on IGA,then construct the reduced basis via finding the degree s of freedom(DOFs)influenced by local modification,and employing the reduced basis to reduce the initial large problem that has N DOFs to small-scaled system that only has S DOFs,in which S is much small than N.So that we only need to solve the reduced small scale system whose scale is only S × S,hence avoiding huge time cost in solving the large-scaled initial problem of,thereby achiving the goal of real-time integration of CAD/CAE analysis.Moreover,we advance and extend the IGA-IC method to efficiently conduct nonlinear analysis.Namely,we reduce the full scaled initial equations in the Newton-Raphson iteration to small scaled equations that only has S DOFs,hence only solving the reduced equation in each Newton-Raphson iteration to significantly improve the efficiency whilst guaranteeing the accuracy.Secondly,focusing on the accuracy aspect,we proposed the IGA-IFU method for the first time to accurately calculate the structure after shape and boundary modifications.The core idea is that the modified equation can be divided into two parts: the equilibrium equation and the unbalanced equation.By using the theory of independent coefficient method,additional constraints are applied to the unbalanced degree of freedom,so that the basic solution of the equilibrium e quation can be obtained by using the SMW formula.Then,a unique solution is derived from the general solution of the equilibrium equation to satisfy the unbalanced equation.This method is derived from the independent coefficient method and Sherman-MorrisonWoodbury(SMW)formula,and the derivation process has no mathematical hypothesis,hence it is an exactly accurate reanalysis method.Thirdly,for the first time,we proposed the method that exactly represents Tailor Rolled Blank(TRB)profile,accurately simulates the TRB,and most importantly,continuously optimizates the thickness based on isogeometric.In this method,the three-dimensional NURBS solid element was first used to accurately represent and simulate TRB,thus avoiding the error caused by i naccurate geometrical model and inappropriate element.The problems existed in traditional TRB optimization are eliminated by the advantages of IGA shape optimization.So that realizing the precise representation of the TRB geometry,the accurate CAE simulation and especially the continuous optimization of thickness that does not rely on the engineers' experience.As well as promoting the development of the TRB and broadening the application of IGA optimization.Lastly,regarding to the structural uncertainty analysis,first,we proposed isogeometric generalized nth perturbation based stochastic method for rapid uncertainty analysis of static and dynamic problems that consider low dimensional uncertainty.The method uses a small perturbation parameter to derive the random input variable and state function as nth order Taylor polynomial expansion near their mean values.It takes full of the advantages that we can increase the n to achieve the higher accuracy and the high accuracy of single DOFs of IGA.Hence,overcomes the issues of the traditional first or second order perturbation based stochastic finite element methods that cannot handle the problems whose variation coefficient of input parameters are large.Second,due to most of the existing literatures only consider onedimensional uncertainty,namely only consider one parameter as random in structure stochastic analysis,and very few studies considered multi-dimensional parameters as random,the author,for the first time,based on the exact representation of problem domain,study material,geometry and force multi-dimensional single uncertainty and the three combined issues.Third,for the material uncertainty analysis,the auhor innotivately consider every material point(element)has independent uncertainty behavior,modelling the practical problems more complexly and authentically.More importantly,we proposed a proper orthogonal decomposition(POD)and monte carlo method(MCS)based isogometic stochastic method to fastly and accurately solv e the multi-dimensional issues mentioned above,especially larger scale the problem is,the more efficient the method will inhert.