• Smart Structures and Systems
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• v.8 no.5
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• pp.433-447
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• 2011

The present paper addresses the nonlinear response of a FG square plate with two smart layers as a sensor and actuator under pressure. Geometric nonlinearity was considered in the strain-displacement relation based on the Von-Karman assumption. All the mechanical and electrical properties except Poisson's ratio can vary continuously along the thickness of the plate based on a power function. Electric potential was assumed as a quadratic function along the thickness direction and trigonometric function along the planar coordinate. By evaluating the mechanical and electrical energy, the total energy equation can be minimized with respect to amplitude of displacements and electrical potential. The effect of non homogenous index was investigated on the responses of the system. Obtained results indicate that with increasing the non homogenous index, the displacements and electric potential tend to an asymptotic value. Displacements and electric potential can be presented in terms of planar coordinate system. A linear analysis was employed and then the achieved results are compared with those results that are obtained using the nonlinear analysis. The effect of the geometric nonlinearity is investigated by using the comparison between the linear and nonlinear results. Displacement-load and potential-load curves verified the necessity of a nonlinear analysis rather than a linear analysis. Improvement of the previous results (by the linear analysis) through employing a nonlinear analysis can be presented as novelty of this study.

• Journal of KSNVE
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• v.8 no.2
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• pp.267-273
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• 1998

This study aims at performing sensitivity analysis of piezoelectric smart structure for minimizing radiated noise from the structure, The structure consists of a flat plate on which disk shaped piezoelectric actuator is mounted, and finite element modeling is used for the structure. The finite element modeling uses a combination of three dimensional piezoelectric, flat shell and transition elements so thus it can take into account the coupling effects of the piezoelectric device precisely and it can also reduce the degrees of freedom of the finite element model. Electric potential on the piezoelectric actuator is taken as a design variable and total radiated power of the structure is chosen as an objective function. The objective function can be represented as Rayleigh's integral equation and is a function of normal displacements of the structure. For the convenience of computation, all degrees of freedom of the finite element equation is condensed out except the normal displacements of the structure. To perform the design sensitivity analysis, the derivative of the objective function with respect to the normal displacements is found, and the derivative of the norma displacements with respect to the design variable is calculated from the finite element equation by using so called the adjoint variable method. The analysis results are compared with those of the finite difference method, and shows a good agreement. This sensitivity analysis is faster and more accurate than the finite difference method. Once the sensitivity analysis program is used for gradient-based optimizations, one could achieve a better convergence rate than non-derivative methods for optimal design of piezoelectric smart structures.

• Smart Structures and Systems
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• v.9 no.2
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• pp.127-143
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• 2012

The present paper deals with the nonlinear analysis of the functionally graded piezoelectric (FGP) annular plate with two smart layers as sensor and actuator. The normal pressure is applied on the plate. The geometric nonlinearity is considered in the strain-displacement equations based on Von-Karman assumption. The problem is symmetric due to symmetric loading, boundary conditions and material properties. The radial and transverse displacements are supposed as two dominant components of displacement. The constitutive equations are derived for two sections of the plate, individually. Total energy of the system is evaluated for elastic solid and piezoelectric sections in terms of two components of displacement and electric potential. The response of the system can be obtained using minimization of the energy of system with respect to amplitude of displacements and electric potential. The distribution of all material properties is considered as power function along the thickness direction. Displacement-load and electric potential-load curves verify the nonlinearity nature of the problem. The response of the linear analysis is investigated and compared with those results obtained using the nonlinear analysis. This comparison justifies the necessity of a nonlinear analysis. The distribution of the displacements and electric potential in terms of non homogenous index indicates that these curves converge for small value of piezoelectric thickness with respect to elastic solid thickness.

• Interaction and multiscale mechanics
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• v.2 no.4
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• pp.413-430
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• 2009

The stator tooth is a key component of the electromechanical integrated toroidal drive system. The stator tooth is spiral in shape and the calculation of its displacements is difficult. In this paper, using the coordinate transformation method, the displacements of the stator tooth in the local coordinate system are expressed as the function of the variable in the drive coordinate system. Using the minimum potential energy principle, the equations of the displacements of the stator tooth under the loads are deduced. The displacement distributions within the stator tooth are investigated and the changes of the displacement distributions along with the main parameters are analyzed. This research can offer the basis for the strength and stiffness design of the drive system.

• Transactions of the Korean Society of Automotive Engineers
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• v.7 no.6
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• pp.198-206
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• 1999

An automobile outside rear view mirror system has been analyzed and designed to reduce vibration with a finite element model. model analysis is conducted for the calculation of natural frequencies. harmonic analysis is utilized to estimate the displacements of the glass surface under dynamic loads. The model is verified with the vibration experiment of the parts and the assembled body. The structure of the mirror system is optimized for the robustness defined by the Taguchi concept. At first, many potential design variables are defined. Final design variables are selected based on the amount of contribution on the objective function. That is, sensitive variables are chose. The SN ratio in the Taguchi method is replaced by an objective function with the mean and the standard deviation of the quality characteristic. The defined objective function is appropriate in the structural design in that the vibration displacements are minimized while the robustness is improved.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.9
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• pp.1779-1786
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• 2002

When the topology optimization is applied to the design of compliant mechanism, unexpected displacements of input and output port are generated since the displacement control is not included in the formulation. To devise a more precise mechanism, displacement constraint is formulated using the mutual potential energy concept and added to multi-objective function defined with flexibility and stiffness of a structure. The optimization problem is resolved by using Finite Element Method(FEM) and Sequential Linear Programming(SLP). Design examples of compliant mechanism with displacement constraint are presented to validate the proposed design method.

• Smart Structures and Systems
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• v.1 no.3
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• pp.309-324
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• 2005

This paper presents an efficient and accurate coupled beam model for piezoelectric bimorphs based on improved first-order shear deformation theory (FSDT). The model combines the equivalent single layer approach for the mechanical displacements and a layerwise modeling for the electric potential. General electric field function is proposed to reasonably approximate the through-the-thickness distribution of the applied and induced electric potentials. Layerwise defined shear correction factor (k) accounting for nonlinear shear strain distribution is introduced into both the shear stress resultant and the electric displacement integration. Analytical solutions for free vibrations and forced response under electromechanical loads are obtained for the simply supported piezoelectric bimorphs with series or parallel arrangement, and the numerical results for various length-to-thickness ratios are compared with the exact two-dimensional piezoelasticity solution. Excellent predictions with low error estimates of local and global responses as well as the modal frequencies are observed.

• Structural Engineering and Mechanics
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• v.45 no.3
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• pp.355-371
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• 2013

Single- and multi-span orthotropic functionally graded hollow cylinders subjected to axisymmetrical bending are investigated on the basis of a unified shear deformable shell theory, in which the transverse displacement is expressed by means of a general shape function. To approach the through-thickness inhomogeneity of the hollow cylinder, a laminated model is employed. The shape function therefore shall be determined for each fictitious layer. To improve the computational efficiency, we resort to a transfer matrix method. Based on the principle of minimum potential energy, equilibrium equations are established, which are then solved analytically using the transfer matrix method for arbitrary boundary conditions. Numerical comparisons among a third-order shear deformable shell theory, an exact elastic theory and the present theory are provided for a simply supported hollow cylinder, from which the present theory turns out to be superior in stress estimation. Distributions of displacements and stresses in single- and three-span hollow cylinders with different boundary conditions are also illustrated in numerical examples.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.2
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• pp.14-22
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• 1995

We treat the vibrations of circular beam and make use of the method employed by J.T.Tielking, which is based on the principle of Hamilton. The Hamilton's principle requires the determinations of the potential and the kinetic energy of the model as well as done by internal pressure forces. Thje potential energy is composed of a part due to elastic deformations of the beam and a part due to radial and tangential displacements of the tread band with respect to the wheel rim. The equations of motion for such a model are derived by reference to conventional energy method. The accuracy of the expressions is demonstrated by comparison of calculated and experimental natural frequencies for circular beam. The circular beam experiences a harmonic, radial excitat- ion acting at a fixed point on the beam. Modal parameters varying the inflation pressure and load are determined experimentally by using the transfer function method.

• Structural Engineering and Mechanics
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• v.62 no.6
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• pp.749-758
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• 2017

In structural mechanics, traditional analyses methods usually employ matrix operations for obtaining displacement and internal forces of the structure under the external effects, such as distributed loads, earthquake or wind excitations, and temperature changing inter alia. These matrices are derived from the well-known principle of mechanics called minimum potential energy. According to this principle, a system can be in the equilibrium state only in case when the total potential energy of system is minimum. A close examination of the expression of the well-known equilibrium condition for linear problems, $P=K{\Delta}$, where P is the load vector, K is the stiffness matrix and ${\Delta}$ is the displacement vector, it is seen that, basically this principle searches the displacement set (or deformed shape) for a system that minimizes the total potential energy of it. Instead of using mathematical operations used in the conventional methods, with a different formulation, meta-heuristic algorithms can also be used for solving this minimization problem by defining total potential energy as objective function and displacements as design variables. Based on this idea the technique called Total Potential Optimization using Meta-heuristic Algorithms (TPO/MA) is proposed. The method has been successfully applied for linear and non-linear analyses of trusses and truss-like structures, and the results have shown that the approach is much more successful than conventional methods, especially for analyses of non-linear systems. In this study, the application of TPO/MA, with Harmony Search as the selected meta-heuristic algorithm, to cables net system is presented. The results have shown that the method is robust, powerful and accurate.