Isogeometric FE-BE method with non-conforming coupling interface for solving elasto-thermoviscoelastic problems

Abstract

The isogeometric finite element (FE) and boundary element (BE) coupling method with non-conforming interface is applied to solve 3D elasto-thermoviscoelastic problems. The thermoviscoelastic constitutive relation is expressed by Stieltjes integral, and the equivalent integral weak form of the problem is derived according to the principle of virtual work, in which the time integral is discretized by the trapezoidal difference approximation formula. The parameters of viscoelastic material are described by Prony series, and the discrete formula can be simplified by recursive relationship to avoid storing all solutions in time steps. The equilibrium and compatibility conditions of FE and BE subdomains on the coupling interface are used to couple two different system matrices, and the coupling of non-conforming non-uniform rational B-splines (NURBS) surfaces in different subdomains is achieved by using virtual knot insertion technique. In addition, the time-temperature equivalent principle is applied to observe the mechanical behavior of viscoelastic materials over a wide temperature range in a short time. Through several numerical examples, the effects of different working conditions and geometrical parameters of combustion chamber on the structure of the solid rocket motor (SRM) are studied, and the correctness and robustness of this method are verified.