Topology Optimization Of Prager-Structures Under Multiple Load Cases Based On Truss-Like Material

The structural topology optimization is always the hotspot and difficulty in thefield of structure optimization research. Compared with the size and the shapeoptimization, although the structural topology optimization problem is more complexand difficult, but its optimization effect is better, and the optimized design scheme ismore economy. In the year of1904, Michell put forward the truss-like continuumtheory, which has been got fast development in recent ten years. It is an importantresearch method in the field of topological optimization.The topology optimization of Prager-structure under different conditions isstudied in this paper. Prager-structure is a special kind of topological optimizationshell structure. Its load has been set in the vertical direction, when the position of theaction line is fixed and the upright position is free. Truss-like continuum materialmodel and finite element method are adopted to study the method to optimize thetopology of plane Prager-structure. It could fix some problems such as numericalinstability or impractical optimization results.At first, a method to optimize the topology of Prager-structure under single loadcases with stress constraints is introduced. The densities and orientations of membersat nodes are taken as design variables. The densities and orientations of the membersat nodes are adjusted according to fully-stressed criterion based on the principalstress direction and the strains along the principal stress direction. The forcedistribution along vertical direction is changed according to the member densitiesdistribution in iteration procedure. The optimal topology of Prager-structure isformed by linking the members, or linking centroid of vertical cross section.Then, an approach is presented to optimize Prager-structures under multipleload cases. Truss-like continuum material model and finite element method areadopted while taking the densities and orientations of members at nodes as designvariables. According to the densities and orientations of each single load cases, thedensities and orientations of multiple load case were defined by a special method.The optimal topology of Prager-structure is formed by linking centroid of verticalcross section.At last, the application of the topology optimization for Prager-structure isdiscussed. The topology optimization of lower steel arch bridge and reticulated shell under half span load are introduced to preliminary design. By the way of structuraltopology optimization, structure stability could be improved and the cost of thestructure could be decreased while the structural safety is kept unchanged.