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This paper proposes an approach for  thermal analysis of articulated systems  subject to boundary and motion constraints (BMC). The solution framework is designed to capture large temperature fluctuations, significant change in geometry due to reference configuration and deformations, and geometric nonlinearity due to  articulated mechanical systems  (AMS) large displacements and spinning motion. Thermal-expansion displacements, which do not contribute to rigid-body translations, are determined from thermal stretch of position-gradient vectors using a new  sweeping matrix technique  designed to eliminate dependence on translational rigid-body modes. A new quadratic  thermal-energy kinetic form  is defined and used to formulate a dynamic force vector that accounts for thermal transient and inertia effects. Nodal thermal displacements are used in formulating AMS differential/algebraic equations (DAEs), and consequently, thermal stresses due to BMC equations are automatically accounted for based on integration of thermal analysis and  Lagrange-D’Alembert principle , which is the foundation of computational  multibody system  (MBS) algorithms. The approach used in this study for large-displacement constrained and unconstrained thermal expansions is based on  multiplicative decomposition  of position-gradient matrix, instead of  strain additive decomposition , for solution of thermo-elasticity problems. Four configurations are used to define continuum geometry and displacements:  straight configuration ,  reference configuration ,  thermal-expansion configuration , and  current configuration . The proposed approach allows applying thermal loads during constrained large displacements, does not impose restrictions on the choice of thermal coefficients, captures reference-configuration geometry and change in inertia forces due to temperature fluctuations, accounts for thermal displacement in formulating AMS nonlinear constraint equations, and allows for integration with MBS algorithms for the study of a wide range of thermo-elasticity problems.

Thermo-elasticity displacement formulation for constrained articulated mechanical systems