梁系结构上限极限分析的弹性模量缩减法

Elastic modulus reduction method for the upper bound limit analysis of beam structures

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。

An upper bound limit analysis method based on beam element and elastic modulus reduction method is proposed.In this method,the element bearing ratio is defined by the generalized yield criterion and the resisting forces of component section,and then the modulus adjustment strategy of elastic modulus reduction method is presented.A series of generalized stress fields and kinematic admissible displacement fields are obtained using structural analysis of beam structures.The formula of the plastic dissipation and elastic strain energy for beam structures is derived by considering the effect of moment and axial force.The upper bound load multiplier of beam structures is proposed.While inherited the merits of simplicity and practicality of the elastic modulus adjustment procedures,the proposed method can be applied to those complex structures with different geometries and material characters.Numerical results show that the method can achieve satisfactory accuracy and iterative stability,and give a solution difference within 4% with analytical solution or other numerical methods within 30 linear elastic iteration steps.