Reanalysis Methods For Topological Modifications Of Structures And Engineering Applications

In the optimization process of an engineering structure, we have to modify thestructure and resolve the displacement or generalized eigenproblem repeatedly inorder to achieve an optimal design. The iterative displacement or vibrationanalysis may be expensive for large and complex structures. Thus, it is necessaryto seek a faster computational method for reanalysis. Reanalysis methods areintended to analyze efficiently structures that are modified due to changes in thedesign. The object is to compute the structural solution for such changes withoutperforming the full analysis. The reanalysis methods usually use the originalsolutions of the original structure.There are various reanalysis methods for static and eigenproblems of modifiedstructures. When changes in design parameters are small, the 1st order and 2ndorder perturbation method can give good approximate solutions. For largechanges in the design, the accuracy of the 1st and 2nd perturbation solutionsoften deteriorates, and they may become meaningless. Thus, it is highly desirableto improve the perturbation method in its accuracy for case of large modificationof the structural parameters. To this end, the perturbation combined with theRayleigh quotient is used to improve the accuracy of eigenvalue reanalysis.Recently, the Pade' approximate and the extended Kirsch combined methodswere used in approximate eigenvalue reanalysis of the modified structures.Topological optimization concerning the topological variations of a structure(number and orientation of elements) is difficult because of changes in thestructural model. The solutions of topological optimization problems are moredifficult because of changes in the structural model. Members and joints aredeleted or added during the solution process and the reanalysis model becomescomplicated. Developing reanalysis procedures for general topologicalmodifications is particularly important when the number of degrees of freedom(DOFs) is modified and the structural response is significantly changed. It seemsthat more efforts are still required in order to implement topologicalmodifications in practical structural design.In this paper, the unified methods of both static and modal reanalysis forstructural topological modifications are disused, and efficient methods arepresented and implement on computers based on general I-DEAS software. Thepaper still forcus on the static and dynamic topological optimization and someeffective methods for topological optimization are developed.In chapter 2, an iterative combined approximate method for static reanalysis ispresented. When the number of iterations is equal to one, the present iterative CAmethod is reduced to the basic CA.In chapter 3, a universal method of structural reanalysis for topologicalmodification is proposed. The presented method is suitable for all three cases oftopological modifications including deletions and additions of members andjoints. In cases when the number of DOFs is increased, it is necessary toestablish the condenced equation by the Guyan reduction such that the newdegrees of freedom are included in the analysis model. The procedure isbasically an approximate two-step method. First, the newly added degrees offreedom (DOFs) are assumed to be linked to the original DOFs of the modifiedstructure by means of the Guyan reduction so as to obtain the condensedequation. Second, the displacements of the original DOFs of the modifiedstructure are solved by using the static reanalysis method discussed in chapter 2.And the displacements of the newly added DOFs resulting from topologicalmodification can be recovered.In chapter 4, the eigensolution reanalysis is discussed. The forcus mainly onextended Kirsch combined method, and selection of the basis vector for thecombined method is proposed. In case of the repeated (or closed) eigenvalue, theeigenvectors of the orinal structure have been recalculated according to theincreasment of the stiffness matrix and mass matrix. As a result, theeigensolution reanalysis method of both repeated and distinct eigenvalue systemcan be deal with in the same way.In chapter 5, a unified method for structural modal reanalysis for three cases oftopological modifications is presented. In this method, the newly added degreesof freedom (DOFs) are linked to the original DOFs of the modified structure bymeans of the dynamic reduction so as to obtain the condensed equation.Furthermore, the extended Kirsch method is used to improve the accuracy of thestarting solutions of the initial structure. And then, the eigenvectors of newlyadded DOFs resulting from topological modification can be recovered. At last,the Rayleigh-Ritz analysis is used to evaluate the eigenvalues and eigenvectorsfor the modified structure. In the present method, the expanded basis vectors areformed by direct decomposition of the matrix ( ΔK mm ?λ 0 iΔMmm) and forwardand backward substitution of the manupulation matrix, just avoid the conditionalconvergence when using iterative perturbation method based on the results of theinitial structure and the accuracy is improved with the extended Kirsch method,where the inverse, , was calculated by the Neumannconvergent series.1( ΔK mm ?λ0 iΔMmm)?In chapter 6, the mass of bus structure was minimized using static topologicaloptimization under multiple loading cases. In order to avoid the tedium solutionof mapping and ill loading cases, the sensitivity of stain energy density waspresented. The non-dimensional measure used for identification of the element tobe removed is given. The optimal procedure is described. In the optimal process,the elements of the structure were divided into two groups: optimizable groupand non-optimizable one. And available stiffeners were added to the structure asto form the base structure. The exact solution of base structure is considered theoriginal solution of the reanalysis method. The structure is modified according tothe non-dimensional measurement of each element, and the reanalysis methodpresented by chapter 3 is used to solve the modified structure. The presentprocedure was implemented for the bus structure, and effective results wereobtained.In chapter 7, the dynamic design of mixer is discussed. An ESO like method isdeveloped. In this method, small section elements are added to the mixerstructure to form the base structure, and the element is recovered according to theelement sensitivity. Using the critiral methods, the torsion strength of thevibrational griddle is improved, and the abnormal diagnal vibration is avoided.Also, the efficiency of griddle is improved using spring parameteral optimization.The fact must be noted that the modified structure is sovled using the modalreanalysis method presented in chater 5.In chapter 8, the impletement of topological reanalysis methods are presented.Base on the open architecture of the CAD/CAE/CAM software, the structure ofthe reanalysis methods is developed, and the core commands and modules of theI-DEAS open solution are discussed.