Coupled electro-elastic analysis of functionally graded piezoelectric material plates

Chih-Ping Wu,Shuang Ding 국제구조공학회 2015 Smart Structures and Systems, An International Jou Vol.16 No.5

A unified formulation of finite layer methods (FLMs), based on the Reissner mixed variational theorem (RMVT), is developed for the three-dimensional (3D) coupled electro-elastic analysis of simply-supported, functionally graded piezoelectric material (FGPM) plates with open- and closed-circuit surface conditions and under electro-mechanical loads. In this formulation, the material properties of the plate are assumed to obey an exponent-law varying exponentially through the thickness coordinate, and the plate is divided into a number of finite rectangular layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations of the primary field variables of each individual layer, respectively, such as the elastic displacement, transverse shear and normal stress, electric potential, and normal electric displacement components. The relevant orders used for expanding these variables in the thickness coordinate can be freely chosen as the linear, quadratic and cubic orders. Four different mechanical/electrical loading conditions applied on the top and bottom surfaces of the plate are considered, and the corresponding coupled electro-elastic analysis of the loaded FGPM plates is undertaken. The accuracy and convergence rate of the RMVT-based FLMs are assessed by comparing their solutions with the exact 3D piezoelectricity ones available in the literature.

Quasi-3D static analysis of two-directional functionally graded circular plates

Chih-Ping Wu,Lu-Ting Yu 국제구조공학회 2018 Steel and Composite Structures, An International J Vol.27 No.6

A weak-form formulation of finite annular prism methods (FAPM) based on Reissner’s mixed variational theorem (RMVT), is developed for the quasi three-dimensional (3D) static analysis of two-directional functionally graded (FG) circular plates with various boundary conditions and under mechanical loads. The material properties of the circular plate are assumed to obey either a two-directional power-law distribution of the volume fractions of the constituents through the radial-thickness surface or an exponential function distribution varying doubly exponentially through it. These FAPM solutions of the loaded FG circular plates with both simply-supported and clamped edges are in excellent agreement with the solutions obtained using the 3D analytical approach and two-dimensional advanced plate theories available in the literature.

Static analysis of multiple graphene sheet systems in cylindrical bending and resting on an elastic medium

Chih-Ping Wu,Chih-Chen Lin 국제구조공학회 2020 Structural Engineering and Mechanics, An Int'l Jou Vol.75 No.1

An asymptotic local plane strain elasticity theory is reformulated for the static analysis of a simply-supported, multiple graphene sheet system (MGSS) in cylindrical bending and resting on an elastic medium. The dimension of the MGSS in the y direction is considered to be much greater than those in the x and z directions, such that all the field variables are considered to be independent of the y coordinate. Eringen’s nonlocal constitutive relations are used to account for the small length scale effects in the formulation examining the static behavior of the MGSS. The interaction between the MGSS and its surrounding foundation is modelled as a Winkler foundation with the parameter kw, and the interaction between adjacent graphene sheets (GSs) is considered using another Winkler model with the parameter cw. A parametric study with regard to some effects on the static behavior of the MGSS resting on an elastic medium is undertaken, such as the aspect ratio, the number of the GSs, the stiffness of the medium between the adjacent layers and that of the surrounding medium of the MGSS, and the nonlocal parameter.

A state space meshless method for the 3D analysis of FGM axisymmetric circular plates

Chih-Ping Wu,Yan-Cheng Liu 국제구조공학회 2016 Steel and Composite Structures, An International J Vol.22 No.1

A state space differential reproducing kernel (DRK) method is developed for the three-dimensional (3D) analysis of functionally graded material (FGM) axisymmetric circular plates with simply-supported and clamped edges. The strong formulation of this 3D elasticity axisymmetric problem is derived on the basis of the Reissner mixed variational theorem (RMVT), which consists of the Euler-Lagrange equations of this problem and its associated boundary conditions. The primary field variables are naturally independent of the circumferential coordinate, then interpolated in the radial coordinate using the early proposed DRK interpolation functions, and finally the state space equations of this problem are obtained, which represent a system of ordinary differential equations in the thickness coordinate. The state space DRK solutions can then be obtained by means of the transfer matrix method. The accuracy and convergence of this method are examined by comparing their solutions with the accurate ones available in the literature.

3D buckling analysis of FGM sandwich plates under bi-axial compressive loads

Chih-Ping Wu,Wei-Lun Liu 국제구조공학회 2014 Smart Structures and Systems, An International Jou Vol.13 No.1

Based on the Reissner mixed variational theorem (RMVT), finite rectangular layer methods (FRLMs) are developed for the three-dimensional (3D) linear buckling analysis of simply-supported, fiber-reinforced composite material (FRCM) and functionally graded material (FGM) sandwich plates subjected to bi-axial compressive loads. In this work, the material properties of the FGM layers are assumed to obey the power-law distributions of the volume fractions of the constituents through the thickness, and theplate is divided into a number of finite rectangular layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations of the field variables of each individual layer, respectively, and an h-refinement process is adopted to yield the convergent solutions. The accuracy and convergence of the RMVT-based FRLMs with various orders used for expansions of eachfield variables through the thickness are assessed by comparing their solutions with the exact 3D and accurate two-dimensional ones available in the literature.

A semi-analytical FE method for the 3D bending analysis of nonhomogeneous orthotropic toroidal shells

Chih-Ping Wu,En Li 국제구조공학회 2021 Steel and Composite Structures, An International J Vol.39 No.3

Based on Reissner’s mixed variational theorem (RMVT), the authors develop a semi-analytical finite element (FE) method for a three-dimensional (3D) bending analysis of nonhomogeneous orthotropic, complete and incomplete toroidal shells subjected to uniformly-distributed loads. In this formulation, the toroidal shell is divided into several finite annular prisms (FAPs) with quadrilateral cross-sections, where trigonometric functions and serendipity polynomials are used to interpolate the circumferential direction and meridian-radial surface variations in the primary field variables of each individual prism, respectively. The material properties of the toroidal shell are considered to be nonhomogeneous orthotropic over the meridian-radial surface, such that homogeneous isotropic toroidal shells, laminated cross-ply toroidal shells, and single- and bi-directional functionally graded toroidal shells can be included as special cases in this work. Implementation of the current FAP methods shows that their solutions converge rapidly, and the convergent FAP solutions closely agree with the 3D elasticity solutions available in the literature.

Exact solutions of free vibration of rotating multilayered FGM cylinders

Chih-Ping Wu,Hao-Yuan Li 국제구조공학회 2012 Smart Structures and Systems, An International Jou Vol.9 No.2

A modified Pagano method is developed for the three-dimensional (3D) free vibration analysis of simply-supported, multilayered functionally graded material (FGM) circular hollow cylinders with a constant rotational speed with respect to the meridional direction of the cylinders. The material properties of each FGM layer constituting the cylinders are regarded as heterogeneous through the thickness coordinate, and then specified to obey a power-law distribution of the volume fractions of the constituents, and the effects of centrifugal and Coriolis accelerations, as well as the initial hoop stress due to rotation, are considered. The Pagano method, which was developed for the static and dynamic analyses of multilayered composite plates, is modified in that a displacement-based formulation is replaced by a mixed formulation, the complex-valued solutions of the system equations are transferred to the real-valued solutions, a successive approximation method is adopted to extend its application to FGM cylinders, and a propagator matrix method is developed to reduce the time needed for its implementation. These modifications make the Pagano method feasible for multilayered FGM cylinders, and the computation in the implementation is independent of the total number of the layers, thus becoming less time-consuming than usual.

3D buckling analysis of FGM sandwich plates under bi-axial compressive loads

Wu, Chih-Ping,Liu, Wei-Lun Techno-Press 2014 Smart Structures and Systems, An International Jou Vol.13 No.1

Based on the Reissner mixed variational theorem (RMVT), finite rectangular layer methods (FRLMs) are developed for the three-dimensional (3D) linear buckling analysis of simply-supported, fiber-reinforced composite material (FRCM) and functionally graded material (FGM) sandwich plates subjected to bi-axial compressive loads. In this work, the material properties of the FGM layers are assumed to obey the power-law distributions of the volume fractions of the constituents through the thickness, and the plate is divided into a number of finite rectangular layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations of the field variables of each individual layer, respectively, and an h-refinement process is adopted to yield the convergent solutions. The accuracy and convergence of the RMVT-based FRLMs with various orders used for expansions of each field variables through the thickness are assessed by comparing their solutions with the exact 3D and accurate two-dimensional ones available in the literature.

Nonlinear vibration analysis of an embedded multi-walled carbon nanotube

Wu, Chih-Ping,Chen, Yan-Hong,Hong, Zong-Li,Lin, Chia-Hao Techno-Press 2018 Advances in nano research Vol.6 No.2

Based on the Reissner mixed variational theorem (RMVT), the authors present a nonlocal Timoshenko beam theory (TBT) for the nonlinear free vibration analysis of multi-walled carbon nanotubes (MWCNT) embedded in an elastic medium. In this formulation, four different edge conditions of the embedded MWCNT are considered, two different models with regard to the van der Waals interaction between each pair of walls constituting the MWCNT are considered, and the interaction between the MWCNT and its surrounding medium is simulated using the Pasternak-type foundation. The motion equations of an individual wall and the associated boundary conditions are derived using Hamilton's principle, in which the von $K{\acute{a}}rm{\acute{a}}n$ geometrical nonlinearity is considered. Eringen's nonlocal elasticity theory is used to account for the effects of the small length scale. Variations of the lowest frequency parameters with the maximum modal deflection of the embedded MWCNT are obtained using the differential quadrature method in conjunction with a direct iterative approach.

Free vibration analysis of bi-directional functionally graded annular plates using finite annular prism methods

Chih-Ping Wu,Lu-Ting Yu 대한기계학회 2019 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.33 No.5

Based on Reissner’s mixed variational theorem, the authors develop a finite annular prism method (FAPM) for the three-dimensional (3D) free vibration analysis of bi-directional functionally graded (FG) annular plates with assorted boundary conditions. In this formulation, the FG annular plate is divided into a number of finite annular prisms with triangular cross-sections, in which Fourier functions and Lagrange polynomials are used to interpolate the circumferential direction and radial-thickness surface variations of primary field variables in each individual prism, respectively. The material properties of the FG annular plate are assumed to obey an exponential function distribution varying doubly exponentially through the radial-thickness surface. These FAPM solutions for the frequency parameters and their corresponding mode shapes of the FG annular plate closely agree with the solutions obtained using other 3D approaches available in the literature.