用勒让德多项式逼近结构的瞬态响应

以勒让德多项式作为结构响应计算的试函数，利用其正交性导出了线性结构的瞬态响应的数学模型，推导中没有对位移响应作时间上的离散，所得的位移响应是一连续函数，与时间离散无关，且无条件稳定，算例表明，该方法具有很高的精度。

Approximation of Transient Structural Response with Legendre Polynomial

The Legendre Polynomial is taken as the trial function for calculation of structural response, and the orthogonality of the function is used for development of a mathematical model for transient response of linear structures. During the deduction, time discretization of displacement response is not performed. The displacement response derived is a continuous function, which is irrelevant with time discretization and stable in any case. Examples show that the present method is of high precision.