【摘要】 对随机参数结构在随机载荷作用下的结构分析、可靠性分析和优化设计等问题进行研究。以桁架结构为对象进行结构分析 ,分别或同时考虑结构材料的物理参数、构件的几何尺寸和作用载荷幅值等的随机性。应用代数综合法对结构响应 (位移、应力 )随机变量的数字特征计算表达式进行推导。在结构可靠性分析的基础上 ,构建以杆件截面积为设计变量 ,使结构重量极小化为目标函数 ,同时具有应力和位移可靠性约束的优化设计数学模型。对模型中的可靠性约束进行等价显示化处理 ;对结构响应进行基于可靠性的灵敏度分析 ,导出结构响应可靠性约束的灵敏度计算公式。通过算例验证了文中提出的基于概率的结构分析和优化设计模型与方法的合理性与可行性更多还原

【Abstract】 Structural reliability analysis and optimization are of great importance in modern engineering structural research and study. This paper mainly deals with the subjects below. The first one is the reliability study of the skeletal structures with some stochastic factors; the second is structural reliability analysis and the last is structural optimization with one or both structural displacements and stresses reliability constraints. In the research of the structural responses analysis and structural optimization, the stochastic factors of the structural physical parameters (such as the Young’s modulus and structural dimensions) and the load applied on structures were all considered. The algebra synthesis method was utilized to develop the numeric characteristic expressions of structural responses (displacements and stresses) that are random variables. We established optimization mathematical models with the structural reliability constraints based on the structural reliability analysis. Truss structures were studied as the research objects and the structural elements cross sectional areas are regarded as the design variables here. In optimization process, the reliability constraints were equivalently displayed so that the constraints in probability form could be shown in normal form. The sensitivity of the structural responses’ reliability constraints with the normal form was also studied and the formulae to compute the sensitivity were also deduced. Finally, the validity and the feasibility of the models and the methods are verified by two numeric examples.更多还原