It is convenient to use the same order of finite elements in the thermal analysis and the relevant thermal stress analysis. But displacement based isoparametric elements with the same order of approximation as the temperature field result in oscillatory stress field. The undesired oscillation can be weakened either by considering stresses only at the reduced integration points or by imposing consistency in the order of approximation.
In this thesis, the consistency is reinforced by enhancing the strains related to deformation. Thermal deformation is introduced into the generalized variational principle of Fellipa and basic equations for the modified enhanced assumed strain method are derived. For the stress approximation of bilinear elements, the 5βversion of Pian and Sumihara is adopted.
In the numerical experiment, the bilinear enhanced assumed strain element is considered. The numerical results for several problems show that the present element behaves well and weakens the oscillation. From the comparison of the results with those of the quadratic element it is concluded that enhanced linear element results in almost the same magnitude of error as the quadratic element but the former is more sensitive to shape distortion than the latter. Future researches will be needed to reduced the sensitivity.
