A Generalized Finite Element Method with Spread and Discrete Enrichments for Capturing High Thermal Gradients in Composites

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Abstract

The demand for composites is rising in industries for instance, in aircraft and automobile engines. In these applications, composites encounter high thermal gradients service condition, and composites exhibit material discontinuous gradient field. It is essential to study how high thermal gradients and material discontinuities influence on the composites’ behavior. Composites are usually modelled with the standard finite element method (FEM), but mesh refinement is required near material interfaces and regions with high thermal gradients to obtain accurate solutions. Enriched finite element procedures are able to solve this issue. The Generalized Finite Element Method (GFEM) can approximate high thermal gradients by adding enriched degrees of freedom (DOFs) to original mesh nodes. In addition, the Interface-enriched Generalized Finite Element Method (IGFEM) can cope with material discontinuities by creating nodes at the intersection between discontinuities and edges of elements in the mesh. Yet, GFEM and IGFEM have their own limitations when implemented: while GFEM needs extra enrichments to resolve the material interfaces in composites, and IGFEM requires mesh refinement if thermal gradients are too high in cut elements. Then we can combine the best of both methods.

In this thesis, a new Generalized Finite Element Method with spread and discrete enrichments (GFEM^sd) is developed to simulate heat transfer problems with high thermal gradients in composites. By combining GFEM and IGFEM formulations, GFEM^sd is capable of dealing with high thermal gradients and material discontinuities simultaneously in an effective manner. We show that GFEM^sd obtains accurate results when compared with analytical solutions in numerical examples. A convergence study illustrates that fewer DOFs are required in GFEM^sd for achieving the same level of accuracy comparable to that of IGFEM. We then apply GFEM^sd to simulate a twill pattern composite and derive effective heat conductivity values. Lastly, based on the composite’s minimum effective heat conductivity, fiber shape optimization is conducted to obtain the best design for a fixed fiber volume fraction.