一种获得各向异性平面梁在任意荷载作用下弹性解的新方法  

A Novel Method to Obtain the Elasticity Solutions of Anisotropic Plane Beam Subjected to Arbitrary Loads

作　　者：张浪[1,2] 李学武[1] 夏建中[1] 

机构地区：[1]国防科学技术大学校务部基建办公室,长沙410073 [2]国防科学技术大学航天科学与工程学院,长沙410073

出　　处：《应用数学和力学》2013年第6期630-642,共13页Applied Mathematics and Mechanics

摘　　要：通过求解函数方程,给出了一种获得各向异性线性平面梁弹性解的新方法,该方法可以考虑任意形式的荷载以及各种端部支撑条件。将该方法与传统的逆解法或者半逆解法比较,其最大的好处在于不需要猜测应力函数的形式而直接获得问题的精确解。算例验证了该方法的正确性,同时也提供了一种求解平面梁承受任意荷载的新思路。A novel method was given to obtain the elasticity solutions for linear anisotropic plane beam subjected to arbitrary loads with various ends conditions by solving functional equa- tions. Comparing this general method with traditional trial-and-error method, the most advan- tage was that there was no need to guess the form of stress function and obtain the solutions di- rectly. The united equations for solving boundary value problem of anisotropic plane beam were found and several examples showed the correctness of this general method. A new way was al- so provided to derive the elasticity solutions of plane beam subjected to arbitrary loads with va- rious ends conditions.

关 键 词：函数方程 各向异性平面梁 弹性解 任意荷载 边界条件 弹性理论 

分 类 号：O343.1[理学—固体力学]