FINITE ELEMENT ANALYSIS OF THERMOELASTIC INSTABILITY OF A RETANGULAR BLOCK ON A RIGID WALL

Abstract

두 물체의 접촉면 사이의 정상상태의 열전달은 열변형을 일으키고 그결과 나타나는 접촉압력의 변화는 열접촉저항 및 열전달을 변화시켜 전체 시스템을 불안정하게 할 수 있다.

섭동법에 의한 이론적 해석방법은 단순한 시스템에 대하여는 가능하지만 유한한 길이의 기하학적 형상을 가진 시스템에 대하여는 매우 어려워진다. 본논문에서는 강체와 열탄성적 접촉을 하고있는 사각블럭의 안정성을 판정하기위해 시간에 따라 지수적으로 변화하는 변수분리 형태의 섭동을 가정하여 지배방정식들을 유한요소식화 하였다. 그 결과 지수증가율에 대한 선형 고유치 문제를 얻을 수 있으며, 시스템은 모든 고유치가 음의 실수부를 가질때 안정하다. 수치적인 해석결과를 강체인 벽과 열탄성적인 접촉을 하고 있는 스트립의 이론적 해석결과와 비교하여 제안한 유한요소법의 타당성을 보였다.

The steady-state conduction of heat across an interface between two contacting bodies can become unstable as a result of the interaction between thermoelastic distortion and a pressure-dependent thermal contact resistance. Analytical solutions for the stability boundary have been obtained for simple systems using perturbation methods, but become prohibitively complex for finite geometries. This paper presents a finite element formulation of the perturbation method, in which the linearity of the governing equations is exploited to obtain separated-variable solutions for the perturbation with exponential variation in time. The problem is thus reduced to a linear eigenvalue problem with the exponential growth rate appearing as the eigenvalue. Stability of the system requires that all eigenvalues have negative real part. The method is tested against an analytical solution of the two-dimensional problem of a strip in contact with a rigid wall. Excellent results are obtained for the stability boundary even with a relatively coarse discretization.

The steady-state conduction of heat across an interface between two contacting bodies can become unstable as a result of the interaction between thermoelastic distortion and a pressure-dependent thermal contact resistance. Analytical solutions for the stability boundary have been obtained for simple systems using perturbation methods, but become prohibitively complex for finite geometries. This paper presents a finite element formulation of the perturbation method, in which the linearity of the governing equations is exploited to obtain separated-variable solutions for the perturbation with exponential variation in time. The problem is thus reduced to a linear eigenvalue problem with the exponential growth rate appearing as the eigenvalue. Stability of the system requires that all eigenvalues have negative real part. The method is tested against an analytical solution of the two-dimensional problem of a strip in contact with a rigid wall. Excellent results are obtained for the stability boundary even with a relatively coarse discretization.