Topology Optimization Method Of Inflatable Membrane Structure Base On Truss-like Material Model

With the application of new materials and new technologies, the spatialstructure appears in a variety of forms. In the past few decades, the membranestructure widely is applied also. Since the difference of design process betweenmembrane structure and traditional structure, it’s the first step to find the shape formembrane structure. In order to determine the shape, in-depth discussion isnecessary. Researchers of countries proposed nonlinear finite element method, forcedensity method, the dynamic relaxation method and so on for form-finding analysis.In recent years, shape-state optimization is introduced. The main work of this paperis to introduce topology optimization method of inflatable membrane and formoptimized the membrane structure in the level of topology based on truss-likematerial model of Prager structure. To this end, the paper describes the basicprinciples of structural topology optimization theory and implementary steps first.Some specific discussions of the numerical instability in discrete structure andcontinuum structure in topology optimization are presented. In order to control thesephenomena, scholars from various countries introduced some methods.The load of membrane structure is not along the vertical direction, butperpendicular to the surface of membrane structure. Due to the position and angle ofthe membrane are to be optimized, so the position and orientation of load areuncertain. The topology optimization of membrane structure is more difficult thanthat of classical Prager structure. In order to introduce the topology optimizationmethod of inflatable membrane which based on truss-like material model of Pragerstructure, this paper introduces numerical methods and optimization models whichwere used in the inflatable membrane structure optimization, and deduces thesensitivities of stiffness matrix of the truss-like material model. This paper solves thequestion of related load of Prager structure by some methods, in order to certify thevalidity of the methods, this paper seeks the smallest volume of the membranestructure by several examples through the design area in plane and space. Only as a theoretical discussion, this thesis uses rectangles in planar problems or cubeelements in space problems. Only the internal pressure of the inflatable membraneand the corresponding prestress are considered. If structural boundary is complex, itneed further processing for the elements. Finally, the thesis points out the furtherwork for topology optimization of inflatable membrane which based on truss-likematerial model of Prager structure.