A Nonclassical Finite Element Approach for the Nonlinear Analysis of Micropolar Plates

2016 ◽  
Vol 12 (1) ◽  
Author(s):  
R. Ansari ◽  
A. H. Shakouri ◽  
M. Bazdid-Vahdati ◽  
A. Norouzzadeh ◽  
H. Rouhi
Keyword(s):  
Finite Element ◽  
Plate Theory ◽  
Nonlinear Modeling ◽  
Three Dimensional ◽  
Mindlin Plate ◽  
Small Scale ◽  
Element Formulation ◽  
Nonlinear Bending ◽  
Finite Element Approach ◽  
Element Approach

Based on the micropolar elasticity theory, a size-dependent rectangular element is proposed in this article to investigate the nonlinear mechanical behavior of plates. To this end, a novel three-dimensional formulation for the micropolar theory with the capability of being used easily in the finite element approach is developed first. Afterward, in order to study the micropolar plates, the obtained general formulation is reduced to that based on the Mindlin plate theory. Accordingly, a rectangular plate element is developed in which the displacements and microrotations are estimated by quadratic shape functions. To show the efficiency of the developed element, it is utilized to address the nonlinear bending problem of micropolar plates with different types of boundary conditions. It is revealed that the present finite element formulation can be efficiently employed for the nonlinear modeling of small-scale plates by considering the micropolar effects.

A Frequency Domain Finite Element Approach for Three-Dimensional Gear Dynamics

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Christopher G. Cooley ◽  
Robert G. Parker ◽  
Sandeep M. Vijayakar
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Frequency Domain ◽  
Dynamic Models ◽  
Three Dimensional ◽  
Static Solution ◽  
System Level ◽  
Element Formulation ◽  
Lumped Parameter ◽  
Element Approach

A finite element formulation for the dynamic response of gear pairs is proposed. Following an established approach in lumped parameter gear dynamic models, the static solution is used as the excitation in a frequency domain solution of the finite element vibration model. The nonlinear finite element/contact mechanics formulation provides an accurate calculation of the static solution and average mesh stiffness that are used in the dynamic simulation. The frequency domain finite element calculation of dynamic response compares well with numerically integrated (time domain) finite element dynamic results and previously published experimental results. Simulation time with the proposed formulation is two orders of magnitude lower than numerically integrated dynamic results. This formulation admits system level dynamic gearbox response, which may include multiple gear meshes, flexible shafts, rolling element bearings, housing structures, and other deformable components.

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