粘弹性固体的精细积分有限元算法

Precise integration finite element algorithm of viscoelastic solid

粘弹性固体本构方程的数学表达式分为微分型和积分型两种,其数值求解主要是时域上离散计算。文中从微分型表达式出发导出其状态空间方程的数学表达式,通过严格推导论证了它与微、积分型表达式的等价性;引入状态空间方程,从而利用精细积分格式来求解粘弹性固体本构方程;给出了粘弹性固体本构方程的精细积分有限元算法,为求解粘弹性固体本构方程的数值解提供了一个新的途径,具有计算简便,求解精度高等优点。

The mathematical representation of viscoelastic solid constitutive equation can be written into the differential equation and integral equation,and their numerical solutions always depend on discrete of time domain.From the differential representation, the mathematical representation of the state space equation deduced, and the equivalence of these equations is given by strictly derivation.Using the state space equation, the constitutive equation can be solved by precise integration.And a precise integration algorithed finite element mothed is proposed. The present algorithm can be used for solving viscoelastic solid constitutive equation and has advantages of high precision and convenient calculation.