针对典型单体结构的数值流形解与弹性力学解对比

针对典型的单体结构悬臂梁的力学行为进行分析。阐述了受集中荷载悬臂梁位移解析公式,利用数值流形方法计算了受集中荷载下悬臂梁的位移情况。将数值计算结果与弹性力学解析解进行对比验证,证明了数值流形方法中加密数学覆盖的收敛性及必要性。通过分析数值计算结果与解析解的误差,表明误差来源于解析解的推导过程,在确定边界条件时解析解忽略了悬臂梁固定端的转动而使解析解存在误差,对解析解的误差提出修正方案并重新与数值解对比,验证了数值流形方法对简单结构体比常规解析解有更高的准确性。

THE CONTRAST OF NUMERICAL MANIFOLD METHOD SOLUTION AND ELASTICITY SOLUTION FOR TYPICAL MONOMER STRUCTURE

For analysis of a typical monomer structure of mechanical behavior, This paper expounds the cantilever beam with concentrated load displacement analytic formula, the numerical manifold method is used to calculate the displacement of cantilever beam under concentrated load. The results of numerical calculation compared with analytical solutions, proved the convergence and necessity of dense mathematical cover in numerical manifold method. Through the analysis of the error between the numerical results and the analytical solution, indicate that the error derived from the analytical solution, analytic solution which ignoring the rotation of fixed end in boundary conditions makes the error exists, the correction scheme of analytical solution is proposed and compared with numerical solution again, to verify the numerical manifold method for monomer structure has higher accuracy than conventional analytic solution.