Mathematical Modeling and Structure Optimization of Cupped Wave Gyro

2013 ◽  
Vol 631-632 ◽  
pp. 1149-1153
Author(s):  
Tao Yi ◽  
Zhi Yong Cheng ◽  
Zhi Sheng Jing ◽  
Ze Long Zhou ◽  
Chao Fa Yu ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Finite Element Method ◽  
Finite Element ◽  
Galerkin Method ◽  
Structure Optimization ◽  
Hamilton Principle ◽  
Modeling Analysis ◽  
Nature Frequency ◽  
Element Method

Cupped wave gyro’s mathematical modeling is derived via Hamilton principle, and the displacement equations and the nature frequency of gyro is determined by Galerkin method. Based on the modeling analysis and finite element method, the parameters of structure are optimized. The paper provides a reference in the design and fabrication of cupped wave gyro.

Natural Frequencies of Rectangular Membrane With Boundary Perturbation

1995 ◽  
Vol 1 (2) ◽  
pp. 139-144 ◽  
Author(s):  
Jamal A. Masad
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Galerkin Method ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Perturbation Approach ◽  
Boundary Perturbation ◽  
The Finite Element Method ◽  
Analytic Expression ◽  
Element Method

A perturbation approach, coupled with the adjoint concept, is used to derive an analytic expression for the natural frequencies of a nearly rectangular membrane. The method is applied for a rectangular membrane with a semicircle at one of the boundaries. The fundamental natural frequency results for this configuration are presented and compared with results from a finite-element method and results from an approximate Galerkin method. The agreement between the fundamental natural frequencies calculated with the perturbation approach and those calculated with the finite-element method improves as the radius of the semicircle decreases and as the semicircle location becomes more eccentric.

Comprehensive Mathematical Modeling and Dynamic Simulation of Fixed Bed Reactor with Finite Element Method

2011 ◽  
Author(s):  
Davood Dehestani ◽  
Hung Nguyen ◽  
Fahimeh Eftekhari ◽  
Jafar Madadnia ◽  
Steven Su ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Simulation ◽  
Fixed Bed ◽  
Fixed Bed Reactor ◽  
Element Method

Topology Optimization of Compliant Mechanisms Based on Interpolation Meshless Method and Geometric Nonlinearity

2019 ◽  
Author(s):  
Yonghong Zhang ◽  
Zhenfei Zhao ◽  
Yaqing Zhang ◽  
Wenjie Ge
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Topology Optimization ◽  
Galerkin Method ◽  
Meshless Method ◽  
Geometric Nonlinearity ◽  
Compliant Mechanism ◽  
Linear Convergence ◽  
The Finite Element Method ◽  
Element Method

Abstract In order to prevent mesh distortion problem arising in topology optimization of compliant mechanism with massive displacement, a meshless Galerkin method was proposed and studied in this paper. The element-free Galerkin method (EFG) is more accurate than the finite element method, and it does not need grids. However, it is difficult to impose complex boundaries. This paper presents a topology optimization method based on interpolation meshless method, which retains the advantages of the finite element method (FEM) that is easy to impose boundary conditions and high accuracy of the meshless method. At the same time, a method of gradually reducing step is proposed to solve the problem of non-linear convergence caused by low-density points in topology optimization. Numerical example shows that these techniques are valid in topology optimization of compliant mechanism considering the geometric nonlinearity, and simultaneously these techniques can also improve the convergence of nonlinearity.

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