COMPARISONS OF THEORETICAL AND FINITE-ELEMENT STRESS-ANALYSIS SOLUTIONS FOR A BIMATERIAL STRIP AND PLATE SUBJECTED TO THERMAL LOADING

A study is made on a bimaterial beam of length 2L and height 2h, composed of a lower half-beam made from material A and an upper half-beam made from material B, under thermal loading. The geometrically identical half-beams are bonded together at the interface. Materials A and B have similar elastic properties, i.e., Young's modulus E( = 207 GPa) and Poisson's ratio nu ( = 0. 3) are the same for both materials but the coefficients of linear thermal expansion are alpha(A) for material A and alpha(B) for material B, where alpha(A) > alpha(B). A theoretical solution based on simple beam theory is derived for the stress-strain-displacement fields at a temperature T1 > T0 where T0 corresponds to an initial stress-free state, when the beam is held at the centre only to prevent rigid-body motion. The main purpose of the investigation is to compare the results of the theoretical solution with those obtained from elastic, plane-stress, finite element analyses, using two different meshes. The case when the ends of the beam are held down is also examined. Finally the analogous axisymmetric problem of a bimaterial circular plate comprising a lower and an upper half-plate bonded together, is investigated and a theoretical solution of the biharmonic equation, using Legendre polynomials, is derived. The results from the theoretical solutions are compared with the results from an axisymmetric finite element analysis and also from a simulation plane-stress analysis using E1 as the effective modulus of elasticity, where E1 = E/(1 - nu), Some interesting features and oddities arising from these investigations are discussed.