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薄壁杆件结构广泛应用于公路桥梁、航空、造船、海洋工程等领域,但其结构分析计算较为复杂,为了得到更好的计算效果,研究了其静力分析的新方法。考虑弯扭耦合作用并重新推导了广义力和广义位移的关系,求解静力下的微分方程组时,把矩阵特征值解法与多项式特征解法结合在一起,得到了用于薄壁结构静力分析计算的有限元精确刚度矩阵。编写了有限元计算程序并引入算例验证,算例的结果表明该方法的计算结果高效、准确,只用很少的有限元单元数目便得到很精确的计算结果。
Thin-walled bar structures are widely used in highway bridges, aviation, shipbuilding, marine engineering and other fields, but the structural analysis and calculation is more complicated. In order to get better calculation results, the new method of static analysis is studied. Considering the interaction between bending force and torsion and deducing the relationship between generalized force and generalized displacement, when solving differential equations under static force, the method of matrix eigenvalue solution and polynomial feature solution are combined to obtain the static analysis of thin-walled structure Calculated Finite Element Accurate Stiffness Matrix. The finite element program was written and the example was verified. The results of the example show that the method is efficient and accurate, and the calculation result is very accurate with only a few finite element units.