陈李子晨, 张春利, 沈旭栋等. 弹性力学平面直梁问题的一种通用求解策略. 力学与实践, xxxx, x(x): 1-6. DOI: 10.6052/1000-0879-24-086
引用本文: 陈李子晨, 张春利, 沈旭栋等. 弹性力学平面直梁问题的一种通用求解策略. 力学与实践, xxxx, x(x): 1-6. DOI: 10.6052/1000-0879-24-086
Chen Lizichen, Zhang Chunli, Shen Xudong, et al. A general strategy for solutions of plane elasticity problems of straight beams. Mechanics in Engineering, xxxx, x(x): 1-6. DOI: 10.6052/1000-0879-24-086
Citation: Chen Lizichen, Zhang Chunli, Shen Xudong, et al. A general strategy for solutions of plane elasticity problems of straight beams. Mechanics in Engineering, xxxx, x(x): 1-6. DOI: 10.6052/1000-0879-24-086

弹性力学平面直梁问题的一种通用求解策略

A GENERAL STRATEGY FOR SOLUTIONS OF PLANE ELASTICITY PROBLEMS OF STRAIGHT BEAMS

  • 摘要: 不同边界条件下狭长等矩形截面直梁在各种荷载作用下的响应分析是弹性力学平面问题教学的主要内容之一。针对直梁的主要边界受多项式载荷作用这一情形,介绍一种通用的理性求解策略,即根据载荷形式确定应力函数形式,进而利用严谨的数学推导一步一步获得多项式形式的弹性力学解析解。针对线性分布荷载作用下一端简支一端固支的直梁,给出了应力函数的解析表达式,通过与基于有限元法的应力计算结果的对比,验证了其正确性。

     

    Abstract: Response analyses of narrow straight beams of uniform rectangular cross-section with different end conditions subject to various loads are the main content of plane problems in the course of elasticity. For the cases of the beam subject to polynomial loads on the main boundaries, a general rational solution strategy is introduced here. The form of stress function is solely determined according to the form of load, based on which an analytical elasticity solution in polynomial form may be derived step-by-step by strict mathematical derivations. For a straight beam subject to a linearly distributed load, with one end simply-supported and the other fixed, the analytical expression for the stress function is presented, with its correctness verified by comparing the theoretical stress results with the finite element modeling.

     

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