Abstract

In this work, a general mathematical models for flexoelectric heterogeneous equilibrium boundary value problems are considered. A methodology to find the local problems and the effective properties of flexoelectric composites with generalized periodicity is presented, using a two-scales asymptotic homogenization method. The model of the homogenized boundary values problem is presented. A procedure to solve the local problems of stratified multilayered composites with wavy geometry with perfect contact at the interface is proposed. Further, a study of a multilayered piezoelectric composite with imperfect contact at the interface and the influence of the flexoelectric constituents in the behavior of heterogeneous structures are investigated. Consequently, simple closed-form formulas for the effective stiffness, piezoelectric, dielectric, and flexoelectric tensors are obtained, based on the solutions of local problems of stratified multilayered composites with perfect contact at the interface. These formulas provide information for the understanding of the symmetry of the homogenized structure. The piezoelectric limit case for rectangular bi-laminated composites is validated. As a numerical example, a bilaminate composite with layers perpendicular to the z-axis is studied. The known results in the literature are used to analyze some numerical cases of piezoelectric composites with non-uniform imperfect contact at the interface (fractures modes) and laminate composites with fibrous reinforcement. Finally, flexoelectric stratified composites with generalized periodicity are studied and discussed.

Notes

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Graduation Date

2021

Semester

Summer

Advisor

Vajravelu, Kuppalapalle

Degree

Doctor of Philosophy (Ph.D.)

College

College of Sciences

Department

Mathematics

Degree Program

Mathematics

Format

application/pdf

Identifier

CFE0008659;DP0025390

URL

https://purls.library.ucf.edu/go/DP0025390

Language

English

Release Date

August 2021

Length of Campus-only Access

None

Access Status

Doctoral Dissertation (Open Access)

Included in

Mathematics Commons

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