热荷载下梁基频和热屈曲临界变温优化设计

摘要

Changing the distribution of the beam cross-sections can change the axial pressure,thus improve fundamental frequency and critical thermal buckling temperature.Beam under thermal load for maximum fundamental frequency and critical thermal buckling temperature is optimized with given volume constraint.Size optimization of the clamped-clamped beam cross-sections shows that optimum frequency increases more significantly under thermal load.With increasing thermal load,the optimum solution of maximum frequency design is similar to the solution of maximum critical thermal buckling temperature design;the optimum solution of maximum critical thermal buckling temperature design is similar to the solution of maximum critical force design.The beam cross-sections distribution of minimum axial pressure is analyzed and the above phenomena are explained.%改变梁截面沿轴线的分布可以改变轴向力,提高梁的基频以及梁热屈曲的临界变温.研究在给定材料体积下,以热荷载作用下梁的基频及屈曲临界变温最大化为目标的优化问题.对两端固支梁截面尺寸优化的研究表明,受热荷载时,采用优化设计可以使频率目标值提高更多;随着热荷载的增大,优化的截面积分布形式与最大化屈曲临界荷载的截面积分布形式更相近;最大化临界变温与最大化轴向力的截面积分布形式非常相似;分析了使轴向力最小的截面积分布,验证了上述现象.