The Third‐Order Shear Deformation Theory for Modeling the Static Bending and Dynamic Responses of Piezoelectric Bidirectional Functionally Graded Plates

Abstract

This work is the first exploration of the static bending and dynamic response analyses of piezoelectric bidirectional functionally graded plates by combining the third-order shear deformation theory of Reddy and the finite element approach, which can numerically model mechanical relations of the structure. The present approach and mechanical model are confirmed through the verification examples. The geometrical and material study is conducted to evaluate the effects of the feedback coefficients, volume fraction parameter, and constraint conditions on the static and dynamic behaviors of piezoelectric bidirectional functionally graded structures, and this work presents a wide variety of static and dynamic behaviors of the plate with many interesting results. There are many meanings that have not been mentioned by any work, especially the working performance of the structure is better than that when the feedback parameter of the piezoelectric component is added, that is, the piezoelectric layer increases the working efficiency. Numerical investigations are the important basis for calculating and designing related materials and structures in technical practice.

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“…With the accelerated pace of urban construction and the continuous rise in the number of cars, the cross-line bridge has become an essential structure to improve city traffic, relieve the pressure of urban traffic and improve the efficiency of road transport [ 1 ]. However, cross-line bridges are often struck by vehicles to varying degrees [ 2 ], which will cause cracks in the girder body and even damage to the steel bars, concrete and post-tensioned strands [ 3 , 4 , 5 ]; as a result, their flexural capacity does not meet the design load specified in the current design specification [ 6 ]. To reduce the effects of traffic on in-service bridges after they undergo collisions, and prevent large areas of traffic paralysis, there is a need for new methods to repair and strengthen or demolish and reconstruct bridges [ 7 ].…”

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