Generalized shell heat transfer element for modeling the thermal response of non-uniformly heated structures

•Formulation of a heat transfer element for non-uniformly heated shells.•Layered formulation based on finite element and control volume techniques.•Proposed element maximizes accuracy and computational efficiency.•Demonstrated improvement over conventional continuum finite elements.

A generalized shell heat transfer element is formulated in isoparametric coordinates to simulate the 3D thermal of non-uniformly heated shells with curved geometries. The element uses a combination of finite element and control volume methods to discretize the domain of the element into 2D layers that are coupled by a finite difference calculation. As demonstrated in previous work, the finite element-control volume formulation allows the thermal response to be evaluated with minimal computational expense and the temperature field is calculated in a manner that is compatible with distributed plasticity elements for structural analysis. Although the formulation uses a mixture of finite element and finite difference equations, the element equations are in a form that can readily be implemented in a commercial finite element code. The nine-node quadratic element considered here is implemented in Abaqus as a user-defined element. One-, two-, and three-dimensional verification cases are presented to demonstrate the capabilities of the element. Comparisons between the shell heat transfer element and traditional continuum heat transfer elements illustrate that the shell element converges rapidly and results in significant savings in computational expense.