The Static Solution for the Layered Piezoelectric Bounded Domain with Side Face Load by the Modified SBFEM (Advances in Applied Mathematics and Mechanics, 2018)
The static response of two-dimensional horizontal layered piezoelectricbounded domain with side face load was investigated. In this paper, the modifiedscaled boundary finite element method (SBFEM) is provided as an effective semi-analyticalmethodology. The method is used to solve the static problem for the layeredpiezoelectric bounded domain. The scaling line definition extends the SBFEM to bemore suitable for analyzing the multilayered piezoelectric bounded domain. It avoidsthe limitations of original SBFEM in modeling the horizontal layered bounded domain.The modified SBFEM governing equation with piezoelectric medium is derivedby introducing Duality variable in the Hamilton system. This derivation technologymakes the progress concise. The novel displacement and electric governing equationsof the modified SBFEM are given together for the first time. The node forces canbe expressed as power exponent function with radial coordinate by introducing theauxiliary variable and using the eigenvalue decomposition. The novel modified SBFEMsolution of layered bounded domain with piezoelectric medium is solved. Thenew power expansion function of layered piezoelectric medium with side face loadis proposed. This technology significantly extends the application range of modifiedSBFEM. The novel treatment of side face load for the layered piezoelectric boundeddomain is proposed. Numerical studies are conducted to demonstrate the accuracy ofproposed technique in handling with the static problem of layered bounded domainwith piezoelectric medium for side face load. The influence of the side face load typeand depth is discussed in detail.