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该文推导了楔形变截面梁弯扭屈曲的非线性应变能,并依据得到的总应变能进行有限元分析公式的推导。对楔形悬臂梁,中间截面最大的楔形变截面简支梁承受集中荷载和均布荷载的情况进行了分析,与ANSYS基于板壳理论的有限元分析结果进行对比,验证了该文理论的正确性和精度。最后依据该文理论分析了两端简支的楔形工字钢梁受不等端弯矩作用下的临界弯矩,拟合了高精度的临界弯矩计算公式,该公式形式与等截面梁的相同,物理意义明确,便于工程应用。
This paper deduces the nonlinear strain energy of the flexural-torsional buckling of a wedge-shaped section beam and derives the finite element analysis formula based on the obtained total strain energy. The wedge-shaped cantilever beam with the largest cross-section of the wedge-shaped cross-section simply supported beam subjected to concentrated load and uniform load were analyzed and ANSYS plate-shell theory based on the finite element analysis of results compared to verify the correctness of the theory of the article And precision. Finally, according to the theory of the paper, the critical moment under unequal bending moment of wedge-shaped I-beam with simply supported ends is analyzed, and the formula of high-precision critical moment is fitted. The same, the physical meaning is clear, easy to engineering applications.