静不定梁的等强度设计
Equi-Strength Design for Statically Indeterminate Beams
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摘要: 本文提出了用最小余能原理对静不定梁进行等强度设计的方法.并就任意分布载荷,集中力或集中力偶作用下的单跨或多跨梁给出了沿梁轴刚度变化的解析表达式.对具有固定宽度可变高度的矩形截面梁和可变外层厚度的夹层梁给出了算例.与已有结果的比较,显示了本方法的有效性.Abstract: In this paper a method for equi-strength design of statically indeterminate beams is presented, based on the principle of minimum complementary energy. And an analytical expression is derived for the stiffness variation of single or multi-span beams under the application of arbitrarily distributed loads, concentrated forces and couples. Illustrated examples concerning beams with fixed width are riabbe height or sandwich beams with variable thickness of outer sheets are also given. The comparison with reported results shows the effectiveness of the proposed method.
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[1] 叶开沅、俞焕然,超静定等强度梁,兰州大学学报,力学专号(1983). [2] 叶开沅,非均匀变厚度弹性体力学的若干问题的一般解,Ⅳ,兰州大学学报,力学专号,1(1979). [3] Washizu,Kyuichiro,Tlariational Methods in Elasticity and Plasticity,third edition(1982). [4] 刘德贵等,《FORTRAN算法汇编》,第一分册,国防工业出版社(1980).
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