A finite element approach for a coupled numerical simulation of fluid-structure-electric interaction in MEMS

In this analyze, a novel finite element coupled algorithm using numerical meth- ods to analyze the interaction between fluid-structure-electric fileds has been presented for piezoelectric actuators. Piezoelectricity is fundamentally an interaction between structure and electric fields. In this paper, at first we analyze the piezoelectric interaction using 3D solid elements and MITC4 shell elements. Solid elements are used for electric analysis and MITC4 shell elements are used for geometric nonlinear structural analysis. The induced electric forces and moment of forces are translated from 3D solid elements to MITC4 shell elements using a novel translation method, and displacements from MITC4 shell elements are translated to 3D solid elements using shell element displacement interpolation func- tions. A projection method is employed in order to solve the interaction between MITC4 shell structure and fluid field

Pseudoelastic mesh–moving using a general scenario of the selective mesh stiffening

The selective mesh stiffening in this study changes the stiffness of the element based on both the element area and shape. It includes the stiffening in the previous studies as a specific case, and leads to a general scenario in the pseudoelastic mesh–moving. This scenario gives better mesh quality in the mesh-moving of a rectangular domain with a structure consisting of a square and a fin undergoes large rotations. This is because the shear deformation of the element is adaptively considered

Microscale electrical contact resistance analysis for resistance spot welding

Electrical contact resistance is an important parameter for resistance spot welding. In this study, a microscale electrical contact resistance analysis method is pro- posed for resistance spot welding. The microscale electrical contact resistance analysis method is combination of an elasto–plastic large deformation contact analysis and an electric current analysis. The electric current analysis is performed for deformed shape of asperity. The tendency of the electrical contact resistance on contact pressure and tem- perature for the electrical contact resistance analysis agrees with that for Babu’s electrical contact resistance model. A multiscale coupled analysis method is also proposed for resistance spot welding. The multiscale analysis consists of macroscale elasto–plastic large deformation contact, electric current and thermal conduction triply coupled analysis and microscale electrical contact resistance analysis. It is confirmed that the resistance spot welding analysis without measurement of electrical contact resistance can be performed by using the microscale electrical contact resistance analysis

Hierarchal decomposition for the structure-fluid-electrostatic interaction in a microelectromechanical system

In this study, a hierarchal decomposition is proposed to solve the structure-fluid-electrostatic interaction in a microelectromechanical system (MEMS). In the proposed decomposition, the structure-fluid-electrostatic interaction is partitioned into the structure-fluid interaction and the electrostatic field using the iteratively staggered method, and the structure-fluid interaction is split into the structure-fluid velocity field and the fluid pressure field using the projection method. The proposed decomposition is applied to a micro cantilever beam actuated by the electrostatic force in air. It follows from the comparisons among the numerical and experimental results that the proposed method can predict the MEMS vibration characteristics accurately

A novel coupling algorithm for the electric field–structure interaction using a transformation method between solid and shell elements in a thin piezoelectric bimorph plate analysis

Thin piezoelectric bimorph cantilever is increasingly employed throughout the field of actuator and sensor applications in the microelectromechanical system (MEMS). Generally for finite element analysis of piezoelectric bimorph cantilever, three–dimensional (3D) solid element can accurately takes into account a linear or quadratic distribution of electric potential over the thickness for various electric configurations of the actuator and sensor applications. As the MEMS structures usually are quite thin and undergo large deformations, shell elements are very well suited for the structural discretization. This paper is focused on the development of a novel coupled algorithm to analyze the electromechanical coupling in a piezoelectric bimorph actuator and sensor using the shell and solid elements to simulate the structural and electric fields, respectively. The electric force induced by the inverse piezoelectric effect is transformed from the solid elements to the shell elements as an equivalent external force and moment, and the resultant displacements are transformed from the shell elements to the solid elements to evaluate the direct piezoelectric effect. Two different approaches were developed to analyze the electric field–structure interaction. In the first approach, for each block Gauss–Seidel (BGS) iteration, multiple full Newton–Raphson (N–R) iterations are executed until the tolerance criteria are satisfied. In the second approach, the BGS and N–R loops are unified into a single loop. A piezoelectric bimorph actuator and sensor were analyzed for various electrical configurations to demonstrate the accuracy of the proposed method

Performance Evaluation of Numerical Finite Element Coupled Algorithms for Structure–Electric Interaction Analysis of MEMS Piezoelectric Actuator

This work presents multiphysics numerical analysis of piezoelectric actuators realized using the finite element method (FEM) and their performances to analyze the structure-electric interaction in three-dimensional (3D) piezoelectric continua. Here, we choose the piezoelectric bimorph actuator without the metal shim and with the metal shim as low-frequency problems and a surface acoustic wave device as a high-frequency problem. More attention is given to low-frequency problems because in our application micro air vehicle’s wings are actuated by piezoelectric bimorph actuators at low frequency. We employed the Newmark’s time integration and the central difference time integration to study the dynamic response of piezoelectric actuators. Monolithic coupling, noniterative partitioned coupling and partitioned iterative coupling schemes are presented. In partitioned iterative coupling schemes, the block Jacobi and the block Gauss–Seidel methods are employed. Resonance characteristics are very important in micro-electro-mechanical system (MEMS) applications. Therefore, using our proposed coupled algorithms, the resonance characteristics of bimorph actuator is analyzed. Comparison of the accuracy and computational efficiency of the proposed numerical finite element coupled algorithms have been carried out for 3D structure–electric interaction problems of a piezoelectric actuator. The numerical results obtained by the proposed algorithms are in good agreement with the theoretical solutions

Hierarchically decomposed finite element method for a triply coupled piezoelectric, structure, and fluid fields of a thin piezoelectric bimorph in fluid

This paper proposes a numerical method for analyzing a thin piezoelectric bimorph in fluid. A hierarchically decomposed finite element method (FEM) is proposed for modeling the triply coupled piezoelectric-structure–fluid interaction. The electromechanical coupling (piezoelectric-structure interaction) behavior in a thin piezoelectric bimorph is described by the classical constitutive equation, the incompressible fluid flows by the Navier–Stokes equation and the structure by the Cauchy equation of motion. The piezoelectric-structure–fluid interaction system is decomposed into subsystems of fluid–structure interaction (FSI) and piezoelectric field, then the piezoelectric field and the FSI are coupled using the block Gauss–Seidel method, the fluid–structure interaction is split into the fluid–structure velocity field and the pressure field using an algebraic splitting and the fluid–structure velocity field is partitioned into fluid velocity field and structure velocity field. Using the proposed method, the resonance characteristics of a piezoelectric bimorph cantilever made of PVDF and PZT-5H material in fluid are investigated for actuation and sensor configurations

Fluid-structure and electric interaction analysis of piezoelectric flap in a channel using a strongly coupled FEM scheme

Electric and Fluid-Structure interaction (EFSI) is a complex coupled multi-physics phenomenon appears in microelectromechanical system (MEMS) when these microdevices are operated in a fluid media. In this study, the EFSI phenomena refer to a combination of electromechanical (electric-structure interaction) coupling and fluid-structure interaction coupling. Both the electromechanical coupling and the fluid-structure interaction can be simulated in a monolithic way or in a partitioned iteration way. In the proposed method the electromechanical coupling is simulated in a partitioned iterative way with separate solvers for the electrical and mechanical equations using block Gauss-Seidel (BGS) iteration method, while the fluidstructure interaction is simulated in a monolithic way by solving the fluid and structure equations simultaneously using a projection method. The proposed algorithm combines these two methods to analyze the strongly coupled EFSI in MEMS. The proposed method is applied to a flexible flap made of piezoelectric bimorph actuator in a converging channel. The EFSI analysis results show a good agreement with FSI results when a very low input bias voltage is applied to the actuator.ECCM-ECFD 2018 ,6th European Conference on Computational Mechanics (Solids, Structures and Coupled Problems: ECCM 6), 7th European Conference on Computational Fluid Dynamics (ECFD 7), 11-15 June 2018, Glasgow, U

Simplified Analysis Method for Vibration of Fusion Reactor Components with Magnetic Damping

This paper describes two simplified analysis methods for the magnetically damped vibration. One is the method modifying the result of finite element uncoupled analysis using the coupling intensity parameter, and the other is the method using the solution and coupled eigenvalues of the single-degree-of-freedom coupled model. To verify these methods, numerical analyses of a plate and a thin cylinder are performed. The comparison between the results of the former method and the finite element tightly coupled analysis show almost satisfactory agreement. The results of the latter method agree very well with the finite element tightly coupled results because of the coupled eigenvalues. Since the vibration with magnetic damping can be evaluated using these methods without finite element coupled analysis, these approximate methods will be practical and useful for the wide range of design analyses taking account of the magnetic damping effect

Numerical instability of magnetic damping problem of elastic plate

Numerical instability occurs in an analysis of a vibration with magnetic damping, or an electromagnetic and structural coupled problem. In this paper, the numerical instability of the coupled analysis is examined by the finite element in time. It is confirmed that the simultaneous method is unconditionally stable even if the magnetic field and the time increment are large. For the staggered method, we obtain the conditions where the numerical instability occur