求解任意外形弹性拱平面弯曲的一种新方法

基于齐次扩容精细积分法,提出了求解复杂载荷作用下任意外形弹性拱平面弯曲的一种新方法。首先,利用曲梁理论导出了微弧段状态向量的一阶常微分矩阵方程;然后,借助多项式逼近将该方程齐次化和系数常数化,得到了相应的半解析解,它可以达到任意要求的计算机精度。通过算例结果比较,有力地说明了本文方法的有效性和先进性。

Novel Method for Solving Plane Bending of Elastic Arches With Arbitrary Profile

Based on the extended homogeneous capacity precision integration method,a novel method was presented for solving plane bending problems of elastic arches with arbitrary profile.Firstly,a matrix ordinary differential equation of first order for state vectors of the elastic arch was derived by using the curve beam theory.Secondly,the above equation was homogenized by means of the polynomial approximation,and then the variable coefficients matrix was approximately transformed into the constant coefficients one.Finally,a semi-analytical solution to the problems under consideration was carried out.Numerical results compared with the existing methods show that the method proposed has more superiority than the FEM.