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结合线弹性梁系有限元法和弹性模量缩减法,提出了梁系结构上限极限的分析方法。该方法根据构件截面广义屈服准则定义了梁系结构的单元承载比,得到了弹性模量缩减法的模量调整策略,利用梁系有限元法构造出了逼近极限状态的广义应力场以及系列机动允许位移场;同时推导出考虑弯矩和轴力共同影响下的梁单元弹性应变能和塑性耗散功计算公式,建立了梁系结构上限荷载乘子迭代算法。该算法继承了弹性模量调整法原理简单、应用方便等优点,并可应用于具有不同几何特性和材料特性构件构成的复杂结构中。算例分析表明:本文算法具有良好的计算精度和迭代稳定性,通常可在30个线弹性迭代步以内得到与解析法或其他算法在4%以内的极限分析结果。
Combined with the finite element method of linear elastic beam system and the elastic modulus reduction method, the analytical method of the upper limit of beam structure is proposed. In this method, the unit bearing ratio of beam structure is defined according to the generalized yield criterion of member cross-section, and the modulus adjustment method of elastic modulus reduction method is obtained. The generalized stress field approaching the limit state and the series of maneuvering The displacements field is allowed. The calculation formulas of elastic strain energy and plastic dissipative work under the common influence of bending moment and axial force are also deduced. The iterative algorithm of upper limit load multiplier of beam structure is established. The algorithm inherits the advantages of simple elastic modulus adjustment method and convenient application, and can be applied to complex structures with different geometrical characteristics and material properties. The case study shows that the proposed algorithm has good computational accuracy and iterative stability. The results of the limit analysis within 4% of the linear or iterative steps are usually obtained within 30 linear elastic iterations.