Constrained LargeDisplacement Thermal Analysis

Abstract

Two different cases are encountered in the thermal analysis of solids. In the first case, continua are not subject to boundary and motion constraints and all material points experience same displacementgradient changes as the result of application of thermal loads. In this case, referred to as unconstrained thermal expansion, the thermal load produces uniform stressfree motion within the continuum. In the second case, point displacements due to boundary and motion constraints are restricted, and therefore, continuum points do not move freely when thermal loads are applied. This second case, referred to as constrained thermal expansion, leads to thermal stresses and its study requires proper identification of the independent coordinates which represent expansion degreesoffreedom. To have objective evaluation and comparison between the two cases of constrained and unconstrained thermal expansion, the referenceconfiguration geometry is accurately described using the absolute nodal coordinate formulation (ANCF) finite elements. ANCF positiongradient vectors have unique geometric meanings as tangent to coordinate lines, allowing systematic description of the two different cases of unconstrained and constrained thermal expansions using multiplicative decomposition of the matrix of positiongradient vectors. Furthermore, generality of the approach for largedisplacement thermal analysis requires using the Lagrange–D'Alembert principle for proper treatment of algebraic constraint equations. Numerical results are presented to compare two different expansion cases, demonstrate use of the new approach, and verify its results by comparing with conventional finite element (FE) approaches.