Research And Software Development On Topological Optimization Of Frame Structures With Buckling Constraint

For the excellent characteristics of obvious force paths and flexible spaceseparation, the frame structures are widely adopted as the main loading structures inthe fields of architectures, manufactures, and so on. Compared with stiffness andstrength, the failure of structural stability will suddenly cause rapid decline of carryingcapacity, consequent collapse and great harms. However, in the field of optimal design,most researchers regard stiffness and strength as the primary constraints, structuralstability is just for verification. In order to get more practical design and explorestructural potential, it is necessary to optimize with stability as constraints. Currently,the buckling constraints have been studied in topology optimization of continuumstructures, but it is rare in topology optimization of frame structures. Thus, there aretheoretical significance and practical value to study topology optimization of framestructures under buckling constraints.Based on the ICM (Independent Continuous and Mapping) method, the theoryand methods of topological optimization for frame structures with bucklingconstraints are studied, and the relevant software was developed on the platform ofthe MSC.Patran&Nastran software. The main contents are shown as follows.(1) The characteristic of buckling constraints was studied by theory derivationand numerical simulation. On the perspective of theory derivation, the geometricstiffness matrix of spatial framework was deducted according to the elementgeometric stiffness matrix of planar framework. An approach was proposed tocalculate element geometric strain energy fast and efficiently, and the explicitexpression of buckling eigenvalue was derived. On the perspective of numericalsimulation, the central difference scheme was used for example design, and therelationship between the buckling eigenvalue and element topology variables wasanalyzed by numerous numerical examples. It was concluded that the bucklingeigenvalue is approximately proportional to element topological variables. Thestatically determinate presumption was proposed based on the conclusion to simplifythe explicit expression of buckling eigenvalue.(2) Based on the ICM method, the filter functions of element weight, elementstiffness matrix and element geometric stiffness matrix were introduced to formulatean optimization model of minimizing structural weight with a buckling eigenvalueconstraint. Two different explicit optimization models were obtained from the twodifferent explicit expressions of the buckling eigenvalue proposed in part (1). Theformulations of the filter functions were discussed. Optimal solutions of the modelswere obtained by a compiled solver based on Matlab. (3) The issues of the optimal threshold and mesh dependency in topologyoptimization were studied. An adaptive searching threshold approach was used todetermine the optimum threshold and the effect of the thresholds on topology resultswas removed. The selection of the filter radius was discussed based on the graphicfiltering method. The issues of checkerboard phenomenon and mesh dependency intopology optimization of frame structures were solved.According to the above models and algorithms, based on the platform ofMSC.Patran and the structural analysis solver of MSC.Nastran, the secondarydevelopment software by the PCL (Patran Command Language) has been made tosolve topology optimization of frame structures with a buckling constraint. The resultsof the numerical examples indicate the validity of the optimization models, thereliability of the proposed methods and the efficiency of the developed software.