A Finite Element Framework for the Thermal Analysis of Solids and Fluids

The lack of a unified continuum-mechanics approach for predicting the thermal displacements of solids and fluids demonstrates the need for a consistent and unified formulation for the continua that include both solids and fluids. In conventional finite-element formulations, volume changes of solids are predicted using a strain-energy approach, while such changes are accounted for in case of fluids using buoyancy forces. Developing a unified thermal-displacement approach for both solids and fluids can be challenging in the presence of motion and boundary kinematic constraints; some of which must be formulated using nonlinear algebraic equations and others can be formulated using a penalty approach. Improper modeling of thermal expansion in the presence of motion and boundary constraints leads to inaccurate prediction of geometry and stresses. This thesis introduces a new approach, which leads to stress-free thermal expansion in case of unconstrained motion by eliminating the rigid-body translational modes of the solids and fluids using a sweeping matrix technique, ensures continuity of the gradients within the continuum, and allows for modeling both uniform and non-uniform thermal expansion. Two different scenarios are considered in this thesis; in the first scenario, the thermal load is applied before the motion is initiated, leading to a stress-free thermally expanded reference configuration, used as the reference in the stress computations. In the second scenario, the thermal loads are applied during the motion, leading to time-dependent thermal displacements and strains. Conventional finite element (FE) formulations lead to stresses in case of free thermal expansion because of using a strain-energy approach to define the thermal displacement. The method proposed in this thesis for predicting the thermal displacement alleviates this problem and does not require using the strain energy in case of solids and does not require using the buoyancy forces in case of fluids. The use of the approach is demonstrated using solid and liquid-sloshing problems in which the systems are subjected to both motion and boundary constraints.

Author dc:creator

• Mahmoud Elbakly (24399668)

• Engineering, Mechanical
• Constrained thermal expansion in articulated systems
• Fluid structure interaction
• Coupled thermo-mechanical analysis

Statement dc:rights

• In Copyright

DOI dc:identifier

https://doi.org/10.25417/uic.32994107.v1

OAI identifier oai:identifier

oai:figshare.com:article/32994107