Chapter 4 – Nonlinear Static and Buckling Analysi of Piezo 4章–非线性静力分析和屈曲分析压电.docVIP

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Chapter 4 – Nonlinear Static and Buckling Analysi of Piezo 4章–非线性静力分析和屈曲分析压电.doc

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Chapter 4 – Nonlinear Static and Buckling Analysi of Piezo 4章–非线性静力分析和屈曲分析压电

Nonlinear Static and Buckling Analysis of Piezothermoelastic Composite Plates: Part 1 – Formulation Balasubramanian Datchanamourtya and George E. Blandfordb aStaff Engineer, Belcan Engineering Group, Caterpillar Champaign Simulation Center, 1901 S 1st Street, Champaign, IL 61820 bDepartment of Civil Engineering, University of Kentucky, Lexington, KY 40506, USA Abstract Part 1 of the paper presents the geometric nonlinear finite element formulation for deformable piezothermoelastic composite laminates using first-order shear deformation theory. Green-Lagrange strain-displacement equations in the von Karman sense represent geometric nonlinearity. Numerical approximation of the nonlinear equations uses a mixed finite element formulation in terms of an independent discretization of the transverse shear stress resultants in addition to the displacement, rotation, and electric potential variables. Thermoelastic and pyroelectric effects are part of the constitutive equations. Hierarchic Lagrangian interpolation functions express the inplane and transverse displacement variations and electric potential variables while approximation of the transverse shear stress resultants at the Gauss quadrature points use standard Lagrangian shape functions. KEYWORDS: mixed finite element, geometric nonlinearity, smart composite, and von Karman Background Piezoelectric materials exhibit the property of generating an electric potential when subjected to mechanical deformations and this phenomenon is the direct piezoelectric effect. The converse piezoelectric effect by which the material changes shape when an electric voltage is applied is widely used in the actuation and control of vibration in mechanical devices. Piezoelectric materials, also known as smart materials, find their application in aerospace structures, piezoelectric motors, ultrasonic transducers, microphones, etc. Configuring smart composite structures involves bonding piezoelectric layers to the top and bottom