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本文有两方面的内容:(1)结合解析方法和数值方法优点,本文提出求解材料非线性系统动力分析的新方法,并推导了相关公式。新方法利用了分段Lagrange插值多项式和Duhamel积分来求解非线性系统动力响应。当动力荷载表示为分段多项式时,在本构关系的每一个直线段上,可以求出Duhamel积分的精确解。再考虑到刚度转换点上位移和速度的连续性,我们就可以在整个时域上给出非线性系统动力响应的精确解。由于有精确解作为基础,因而和逐步积分法相比,本文方法不但具有较高的计算精度,大大减少了计算工作量,而且彻底地避免了许多数值方法所常遇到的收敛性和稳定性问题。(2)本文提出在原有单层工业厂房结构的侧面加设斜拉杆的抗震加固改造方案,并将此计算方法应用于它的抗震加固计算中。
This article has two aspects: (1) Combining the advantages of analytical method and numerical method, this paper presents a new method to solve the dynamic analysis of material nonlinear system, and deduces the related formula. The new method uses piecewise Lagrange interpolation polynomials and Duhamel integrals to solve the nonlinear system dynamic response. When dynamic loads are expressed as piecewise polynomials, an exact solution to Duhamel’s integral can be found on each straight line of the constitutive relationship. Considering the continuity of displacement and velocity at the stiffness transition point, we can give an exact solution of the nonlinear system dynamic response over the entire time domain. Due to the existence of exact solutions, the proposed method not only has high computational accuracy, greatly reduces computational workload, but also completely avoids the convergence and stability problems commonly encountered in many numerical methods, compared with the stepwise integral method . (2) In this paper, an aseismic retrofit scheme is proposed to add diagonal tie rods to the side of the original single-story industrial plant structure, and this method is applied to the calculation of its aseismic reinforcement.