目前的连续体优化设计通常局限于局部优化和材料拓扑优化，工程应用可行性偏弱。此外，基于满应力的优化设计对复杂荷载形式和材料非线性特征的考虑不够充分，无法直接指导结构弹塑性优化设计。基于工程结构的力学特征、几何形状和荷载模式，探究连续体的截面及形状优化的理论方法和力学解析解具有重要的理论和工程价值。将工程结构等效为变截面连续悬臂梁，将风荷载和地震作用等复杂荷载简化为均布荷载、倒三角荷载和与惯性力相关荷载三种荷载分布形式，针对具有圆环形和箱形等典型横截面的结构，根据满应力理念将结构沿高度方向应力相等或相近作为优化目标，通过建立截面弯矩的不同表征形式并考虑材料非线性研究面向满应力优化的连续结构截面优化理论和解析形式。同时给出结构最优刚度分布解析表达。通过有限元分析对理论方法和结果的正确性进行充分验证，研究结果表明：在结构弹性阶段及塑性阶段，按解析解结果设计截面尺寸的结构均可实现满应力理念；在静力和动力作用下，优化结果均有良好效果；不同荷载形式和截面类型下的最优截面尺寸分布及最优刚度分布是不同的，应根据工程需求进行具体优化设计。
Abstract
The current continuum optimization design mainly focuses on local optimization and material topology optimization, and the feasibility of its engineering application is insufficient.In addition, in the full stress optimization design, the complex load patterns and material nonlinearity are not comprehensively considered.Hence, the traditional methods are difficult to directly guide the structural elastic-plastic optimization design.It is of great theoretical and engineering value to explore theoretical methods and analytical solutions for the optimization of section and shape of continuum based on the mechanical characteristics, geometric shape and load pattern of engineering structures.In the study, engineering structures were regarded as continuous cantilever beams with variable cross-section, and the complex loads such as wind and seismic excitation were simplified as one of three load distribution patterns including uniform load, inverted triangle load and inertia force-related load.According to the concept of full stress, the optimization objective of the structure with typical cross sections such as circular and box shapes is set as that with the same or similar normal stress along the height direction.The section optimization theory and analytical form for optimal continuous structures were explored through establishing different representation forms of section bending moments and considering material nonlinearity.Furthermore, the analytical expression of the optimal stiffness distribution of the structure was given.The example results show that the full stress criterion can be realized in both the elastic and plastic stages when the section size is designed according to the analytical results.The optimization results are effective under both static and dynamic loads.The optimal section size distribution and the optimal stiffness distribution are different for various load patterns and section types, so,the specific continuum optimization design for engineering structures should be carried out according to specific engineering requirements.
关键词
满应力 /
等应力 /
优化设计 /
非线性结构 /
荷载形式 /
刚度分布
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Key words
full stress /
equal stress /
optimal design /
nonlinear constitutive /
load pattern /
stiffness distribution
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