Finite element analysis of micromorphic and micropolar continua based on two-dimensional elasticity

2018 ◽  
Vol 24 (6) ◽  
pp. 1893-1907 ◽  
Author(s):  
Majid Bazdid-Vahdati ◽  
Mohammad Faraji Oskouie ◽  
Reza Ansari ◽  
Hessam Rouhi
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Test Problems ◽  
Element Formulation ◽  
Two Dimensional ◽  
Element Analysis ◽  
Micropolar Continua ◽  
Element Approach ◽  
Micro Deformation ◽  
2D Elasticity

In this paper, within the framework of two-dimensional (2D) elasticity, a novel finite element formulation is proposed based on the micropolar theory (MPT) and the micromorphic theory (MMT). First, general formulations are developed for the micromorphic and micropolar continua in the context of 2D elasticity. Then, they are presented in a matrix form which is useful from the computational viewpoint. In the next step, using the matricized MPT and MMT formulations, a linear finite element approach including the effects of micro-deformation and micro-rotation degrees of freedom (DOFs) of material particles is developed, and a quadratic size-dependent element is proposed accordingly. Two test problems are solved to reveal the efficiency of the developed formulation. The influence of the length scale parameter on the bending of micromorphic and micropolar plates is illustrated in the given examples. Furthermore, comparisons are made between the results obtained from classical elasticity theory and those calculated based upon MPT and MMT.

Substructuring Developments in the Energy Finite Element Formulation

2006 ◽  
Author(s):  
Geng Zhang ◽  
Nickolas Vlahopoulos ◽  
Jiulong Sun
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Simulation Models ◽  
Element Formulation ◽  
System Of Equations ◽  
Element Analysis ◽  
Global System ◽  
Computational Capability ◽  
New Development ◽  
Energy Finite Element Analysis

In Naval applications of the Energy Finite Element Analysis (EFEA) there is an increasing need for developing comprehensive models with a large number of elements which include both structural and interior fluid elements, while certain parts of the structure are considered to be exposed to an external heavy fluid loading. In order to accommodate efficient computations when using simulation models with a large number of elements, joints, and domains, a substructuring computational capability has been developed. The new algorithm is based on dividing the EFEA model into substructures with internal and interface degrees of freedom. The system of equations for each substructure is assembled and solved separately and the information is condensed to the interface degrees of freedom. The condensed systems of equations from each substructure are assembled in a reduced global system of equations. Once the global system of equations has been solved the solution for each substructure is pursued. Important issues which have been considered in the new development originate from the necessity to define substructure interfaces along joint locations. The discontinuity of the energy density variables and the proper formulation of the joints across substructure interfaces have been considered in the new algorithm. In order to demonstrate the validity of the developments and the computational savings a set of previous applications where simulation results were compared to test data is repeated using the substructuring algorithm.

scholarly journals A \(C^1\) bending element for composite plates based on a high-order shear deformation theory

2008 ◽  
Vol 30 (4) ◽  
Author(s):  
Tran Ich Thinh ◽  
Ngo Nhu Khoa ◽  
Do Tien Dung
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Degrees Of Freedom ◽  
Plate Theory ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Element Formulation ◽  
Element Analysis ◽  
Stress Boundary Conditions ◽  
Stress Boundary

A new \(C^1\) rectangular element is proposed and the finite element formulation based on Reddy’s higher-order shear deformation plate theory is developed. Although the plate theory is quite attractive but it could not be exploited as expected in finite-element analysis. This is due to the difficulties associated with satisfaction of inter-elemental continuity requirement and satisfy zero shear stress boundary conditions of the plate theory. In this paper, the proposed element is developed where Reddy’s plate theory is successfully implemented. It has nine nodes and each node contains 7 degrees of freedom. The performance of the element is tested with different numerical examples, which show its precision and range of applicability.

scholarly journals Finite Element Analysis of Fluid-Conveying Timoshenko Pipes

1995 ◽  
Vol 2 (3) ◽  
pp. 247-255 ◽  
Author(s):  
Chih-Liang Chu ◽  
Yih-Hwang Lin
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Virtual Work ◽  
Element Formulation ◽  
Fluid Inertia ◽  
Element Analysis ◽  
Hermitian Interpolation ◽  
Distributed Forces ◽  
Work Done ◽  
Moving Fluid

A general finite element formulation using cubic Hermitian interpolation for dynamic analysis of pipes conveying fluid is presented. Both the effects of shearing deformations and rotary inertia are considered. The development retains the use of the classical four degrees-of-freedom for a two-node element. The effect of moving fluid is treated as external distributed forces on the support pipe and the fluid finite element matrices are derived from the virtual work done due to the fluid inertia forces. Finite element matrices for both the support pipe and moving fluid are derived and given explicitly. A numerical example is given to demonstrate the validity of the model.

Finite Element Analysis of Kinematics and Dynamics of Linkages

2005 ◽  
Author(s):  
Jiaxin Zhao
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Angular Position ◽  
Finite Element Formulation ◽  
Kinematics And Dynamics ◽  
Element Formulation ◽  
Element Analysis ◽  
Joint Forces ◽  
Element Approach ◽  
Close Form

The kinematics and dynamics of two dimensional linkages is analyzed using an uniformed finite element approach in this paper. Each link in the linkage is a naturally discretized finite element and the joints are the nodes connecting elements. The analysis consists of two parts, namely the kinematics part and the dynamics part. In the first kinematics part, positions, linear velocities and linear accelerations of the joints are used as the solution variables in the finite element formulation. In order to have close-form solutions, the linkage must have only one degree of freedom. These joint variables are then solved for each input link configuration of angular position, velocity and acceleration. The angular positions, velocities and accelerations of the other links are then calculated from the joint variables. The position, linear velocity and acceleration of any point on the linkage, like the center of gravity for a particular link, can also be determined if desired. The second dynamics part uses joint forces as the solution variables in the finite element formulation. In each element, a third node is also defined to allow an external force or torque to be applied. Based on the solutions in the first kinematics part, the joint forces are solved for each input configuration. The forces inside each link can then be determined from the joint forces. A MATLAB program is developed for this finite element analysis on general four bar linkages and is posted on the author’s webpage.

Finite-Element Analysis for a Timoshenko Beam Subjected to a Moving Mass

2006 ◽  
Vol 220 (5) ◽  
pp. 669-678 ◽  
Author(s):  
P Lou ◽  
G-L Dai ◽  
Q-Y Zeng
Keyword(s):  
Finite Element ◽  
Timoshenko Beam ◽  
Present Method ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Element Formulation ◽  
Moving Mass ◽  
Element Analysis ◽  
Assumed Mode Method ◽  
Various Boundary Conditions

This article presents a finite-element formulation of a Timoshenko beam subjected to a moving mass. The beam is discretized into a number of simple elements with four degrees of freedom each. The inertial effects of the moving mass are incorporated into a finite-element model. The equation of motion in matrix form with time-dependent coefficients for a Timoshenko beam subjected to a moving mass is derived from the variational approach. The equation is solved by the direct step-by-step integration method to obtain the dynamic response of a Timoshenko beam and the contact force between the moving mass and the beam. The correctness of this present method is validated by means of comparison with the solution obtained by the assumed-mode method. The present method can be effectively used in computation for a Timoshenko beam with various boundary conditions. Numerical simulations are performed to demonstrate the efficiency of the present method.

scholarly journals A Finite Element Approach to the Analysis of Rotating Bladed-Disk Assemblies Coupled With Flexible Shaft

1994 ◽  
Author(s):  
Wen Zhang ◽  
Wenliang Wang ◽  
Hao Wang ◽  
Jiong Tang
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Coupled System ◽  
Equation Of Motion ◽  
Coupled Systems ◽  
The Finite Element Method ◽  
Bladed Disk ◽  
Modal Synthesis ◽  
Element Approach ◽  
Final Equation

A method for dynamic analysis of flexible bladed-disk/shaft coupled systems is presented in this paper. Being independant substructures first, the rigid-disk/shaft and each of the bladed-disk assemblies are analyzed separately in a centrifugal force field by means of the finite element method. Then through a modal synthesis approach the equation of motion for the integral system is derived. In the vibration analysis of the rotating bladed-disk substructure, the geometrically nonlinear deformation is taken into account and the rotationally periodic symmetry is utilized to condense the degrees of freedom into one sector. The final equation of motion for the coupled system involves the degrees of freedom of the shaft and those of only one sector of each of the bladed-disks, thereby reducing the computer storage. Some computational and experimental results are given.

scholarly journals Are Suprapectineal Quadrilateral Surface Buttressing Plates Performances Superior to Traditional Fixation? A Finite Element Analysis

2021 ◽  
Vol 11 (2) ◽  
pp. 858
Author(s):  
Mara Terzini ◽  
Andrea Di Pietro ◽  
Alessandro Aprato ◽  
Stefano Artiaco ◽  
Alessandro Massè ◽  
...  
Keyword(s):  
Finite Element ◽  
Movement Analysis ◽  
High Energy ◽  
Clinical Analysis ◽  
Acetabular Fractures ◽  
Element Analysis ◽  
Bone Stress ◽  
Interfragmentary Movement ◽  
Element Approach ◽  
Transverse Fractures

Acetabular fractures have a high impact on patient’s quality of life, and because acetabular fractures are high energy injuries, they often co-occur with other pathologies such as damage to cartilage that could increase related morbidity; thus, it appears of primary importance developing reliable treatments for this disease. This work aims at the evaluation of the biomechanical performances of non-conservative treatments of acetabular fractures through a finite element approach. Two pelvic plates models (the standard suprapectineal plate—SPP, and a suprapectineal quadrilateral surface buttressing plate—SQBP) were analyzed when implanted on transverse or T-shaped fractures. The plates geometries were adapted to the specific hemipelvis, mimicking the bending action that the surgeon performs on the plate intraoperatively. Implemented models were tested in a single leg stance condition. The obtained results show that using the SQBP plate in transverse and T-shaped acetabular fractures generates lower bone stress if compared to the SPP plate. Interfragmentary movement analysis shows that the SQBP plate guarantees greater stability in transverse fractures. In conclusion, the SQBP plate seems worthy of further clinical analysis, having resulted as a promising option in the treatment of transverse and T-shaped acetabular fractures, able to reduce bone stress values and to get performances comparable, and in some cases superior, to traditional fixation.

Two-Dimensional Full-Vectorial Finite Element Analysis of NRD Guide Devices

2021 ◽  
Vol 31 (4) ◽  
pp. 345-348
Author(s):  
Yasuhide Tsuji ◽  
Keita Morimoto ◽  
Akito Iguchi ◽  
Tatsuya Kashiwa ◽  
Shinji Nishiwaki
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Two Dimensional ◽  
Element Analysis ◽  
Nrd Guide

Effective Convergence Checks for Verifying Finite Element Stresses at Three-Dimensional Stress Concentrations

2018 ◽  
Vol 3 (3) ◽  
Author(s):  
J. R. Beisheim ◽  
G. B. Sinclair ◽  
P. J. Roache
Keyword(s):  
Finite Element ◽  
Error Estimation ◽  
A Posteriori Error Estimates ◽  
Three Dimensional ◽  
Posteriori Error ◽  
Test Problems ◽  
A Posteriori ◽  
Stress Concentrations ◽  
Element Analysis ◽  
A Posteriori Error

Current computational capabilities facilitate the application of finite element analysis (FEA) to three-dimensional geometries to determine peak stresses. The three-dimensional stress concentrations so quantified are useful in practice provided the discretization error attending their determination with finite elements has been sufficiently controlled. Here, we provide some convergence checks and companion a posteriori error estimates that can be used to verify such three-dimensional FEA, and thus enable engineers to control discretization errors. These checks are designed to promote conservative error estimation. They are applied to twelve three-dimensional test problems that have exact solutions for their peak stresses. Error levels in the FEA of these peak stresses are classified in accordance with: 1–5%, satisfactory; 1/5–1%, good; and <1/5%, excellent. The present convergence checks result in 111 error assessments for the test problems. For these 111, errors are assessed as being at the same level as true exact errors on 99 occasions, one level worse for the other 12. Hence, stress error estimation that is largely reasonably accurate (89%), and otherwise modestly conservative (11%).

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