弹、粘性体动力学变分原理的Laplace变换形式、有限元构式及数值方法

作者在1]文中提出了弹、粘动力学变分原理的谱分解形式,本文将其推广到Laplace变换形式,具体写出了薄壳动力学的混合变分原理以及弹-粘-孔隙介质力学的变分原理,并对后者作出了有限元构式. Laplace变换形式的变分原理具有简洁形式,为便于有限元法计算,当已知Laplace变换式的有限个值时,需求原时间函数的有限个值,对此当前尚无成熟方法,本文提供了求原函数的数值方法.从例题可见,这种数值方法是有效的. 结合以上两种理论:从变分原理进行有限元构式以及求Laplace反变换的数值方法,可以使相当广的一类固体动力学问题能够用电子计算机进行求解.

Variational Principles of Elastic-Viscous Dynamics in Laplace Transformation Form,F. E. M. Formulation and Numerical Method

The authbr gives variatioaal principles of elastic-viscous damics is spectral resolving formula, it will be eatended to Laplace traasformetioa forte is this paper, mined variational principle of shell dynamics and variational principle of dynamics of dynamics of elastic-viscous-porous media are concerned,for the.later F., E. M. formulation is worked out.Variatioaal principles is Laplace transformation force have concise forms, for the sake of utilizing F, E. M. conveniently, it is necessary.to find out the values of preliminary time function at some instants, when values,of Laplace transformation at some points are known, but there are no efficient methods till now. In this paper, a aumerival method for finding discrete values of preliauaary function is presented, from numerical wzgmnles, we see such a method is efficient.By corubiaiag. both methods,stated above, variatioaal principles is Laplace transformatioa form and:numerical method,quite wide district of solid, dynamic problems can be solved by the aid of digital computers.