Analysis of electrostatic MEMS using meshless local Petrov–Galerkin (MLPG) method

Meshless Local Petrov-Galerkin Method for Solving Contact, Impact and Penetration Problems

“…Remarkable successes of the MLPG method have been reported in solving the convection-diffusion problems; fracture mechanics; Navier-Stokes flows; and plate bending problems. Recently, the MLPG method has made some strides, and it is applied successfully in studying strain gradient materials [Tang, Shen and Atluri, (2003)), three dimensional elasticity problems ], and elstodynamics [Batra, Ching (2002)]. The MLPG method was also extended to solve the boundary integral equations , and Han, Atluri (2003)].…”

“…The MLPG method, a truly meshless method developed by Atluri and his colleagues, is a simple and lesscostly alternative to the FEM and BEM , Atluri and Shen (2002a, b)]. Remarkable successes of the MLPG method have been reported in solving the convection-diffusion problems [Lin and Atluri (2000)]; beam problems [Raju, Phillips (2003)]; fracture mechanics [Kim & Atluri (2000), Ching & Batra (2001)]; strain gradient materials [Tang, Shen and Atluri, (2003)]; three dimensional elasticity problems ]; elstodynamic problems [Batra, Ching (2002);]; elastodynamic problems in continuously nonhomogeneous solids [Sladek, Sladek, Zhang (2003)]; thermoelasticity ]; Navier-Stokes flows ]; and plate bending problems , Long and Atluri (2002), Qian, Batra, and Chen (2003a, b)]. A comparison study of the efficiency and accuracy of a variety of meshless trial and test functions is presented in Atluri and Shen (2002a, b), based on the general concept of the meshless local PetrovGalerkin (MLPG) method.…”

“…Remarkable successes of the MLPG method have been reported in solving the convection-diffusion problems [Lin and Atluri (2000)]; fracture mechanics [Batra and Ching (2002)]; Navier-Stokes flows ]; and plate bending problems [Long and Atluri (2002)]. Recently, the MLPG method has made some strides, and it is applied successfully in studying strain gradient materials [Tang, Shen and Atluri, (2003)), three dimensional elasticity problems , Han and Atluri (2004a)], elstodynamics [Han and Atluri (2004b)], and multiscale structure and nanomechanics Atluri (2004, 2005)].…”

An Accurate Study on Capacitive Microphone with Circular Diaphragm Using a Higher Order Elasticity Theory

“…Both forces are increased by raising voltage until the applied voltage is touched to a critical value, in which the diaphragm collapses on the fixed electrode which means pull-in happens (Batra et al, 2008). The critical voltage associated with this instability is called pull-in voltage (Batra et al, 2006). In some cases, delaying the onset of pull-in instability would be extremely desirable as it is considered as a limiting factor of the functional range of capacitive microphone.…”

The Meshless Local Petrov-Galerkin Method for Large Deformation Analysis of Hyperelastic Materials

“…It offers a lot of flexibility to deal with large deformation problems. Remarkable successes of the MLPG method have been reported in solving the potential problems, the convection-diffusion problems and the nonlinear boundary value problems by Atluri et al [13][14][15]; the fracture mechanics problems by Kim and Atluri [16]; the NavierStokes flows by Lin and Atluri [17]; the elasticity problems and plate bending problems by Long [18,19]; static and free vibration analysis of thin plates by Gu and Liu [20]; Crack Tip Fields problems by Ching and Batra [21,22]; anisotropic elasticity problems and crack analysis in 3-D axisymmetric FGM bodies by Sladek et al [23,24]. However, there exist some inconveniences in the MLPG method when the shape functions are obtained from interpolation schemes, such as the Moving Least Squares method (MLS), Partition of Unity Method (PUM), Reproducing Kernel Particle Method (RKPM), or Shepard function.…”