工程结构极限承载力上限分析的弹性模量缩减法

ELASTIC MODULUS REDUCTION METHOD FOR THE UPPER BOUND OF ULTIMATE BEARING CAPACITY OF STRUCTURES

基于弹性模量缩减法和基准体法,建立了工程结构极限承载力上限分析的方法。该法结合弹性有限元法进行迭代分析,以广义屈服函数表达的单元承载比作为弹性模量调整的控制参数,根据单元承载比均匀度确定模量调整的阀值——基准承载比,利用单元应变能转化中的能量守恒原理建立单元弹性模量调整策略,通过缩减高应力单元的弹性模量模拟结构弹塑性损伤过程,构造出一系列机动允许位移场,然后利用基准体的上限荷载计算方法,求解出结构极限承载力上限。该方法继承了弹性模量调整法原理简单、应用方便的优点,同时显著提高了计算效率,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:该文算法具有良好的计算精度、收敛性和迭代稳定性。

A numerical solution procedure is presented for the upper bound of ultimate bearing capacity of structures based on the elastic modulus reduction method （EMRM） and the reference volume method. The element bearing ratio （EBR） is developed based on the generalized yield criterion, and is taken as the governing parameter in the process of modulus reduction. The reference EBR is presented by means of the degree of uniformity （DOU） of the EBR. The modulus adjustment strategy is proposed based on the principle of strain energy transformation and energy conservation. A series of kinematic admissible displacement fields are obtained when the damage process of structure is simulated by the iteration process. The reference volume method is introduced to acquire the upper bound of limit load. While inheriting the merits of simplicity and practicality of the elastic modulus adjustment procedures, the method proposed can improve the computational efficiency and enlarge the range of application. Numerical examples show that it is feasible and efficient in limit analysis of complex structures.