An Exact Three-Dimensional Beam Element With Nonuniform Cross Section

2010 ◽  
Vol 77 (6) ◽  
Author(s):  
M. Jafari ◽  
M. J. Mahjoob
Keyword(s):  
Cross Section ◽  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Direct Method ◽  
Three Dimensional ◽  
Curved Beams ◽  
Element Analysis ◽  
Shear Loads ◽  
Line Passing ◽  
Exact Stiffness Matrix

In this paper, the exact stiffness matrix of curved beams with nonuniform cross section is derived using direct method. The considered element has two nodes and 12 degrees of freedom, with three forces and three moments applied at each node. The noncoincidence effect of shear center and center of area is also considered in this element. The deformations of the beam are due to bending, torsion, tensile, and shear loads. The line passing through center of area is a general three-dimensional curve and the cross section properties may change arbitrarily along it. The method is extended to deal with distributed loads on the curved beams. The stiffness matrix of some selected types of beams is determined by this method. The results are compared (where possible) with previously published results, simple beam finite element analysis and analytic solution. It is shown that the determined stiffness matrix is exact and that any type of beam can be analyzed by this method.

scholarly journals Nonlinear Mechanics of Beams With Partial Piezoelectric Layers

2019 ◽  
Vol 86 (10) ◽  
Author(s):  
Hamed Farokhi ◽  
Mergen H. Ghayesh
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Coupled Model ◽  
Beam Theory ◽  
Internal Resonances ◽  
Element Analysis ◽  
Nonlinear Dynamical ◽  
Dimensional Finite Element ◽  
Resonant Region ◽  
Three Dimensional Finite Element

Abstract This paper investigates the nonlinear static response as well as nonlinear forced dynamics of a clamped–clamped beam actuated by piezoelectric patches partially covering the beam from both sides. This study is the first to develop a high-dimensional nonlinear model for such a piezoelectric-beam configuration. The nonlinear dynamical resonance characteristics of the electromechanical system are examined under simultaneous DC and AC piezoelectric actuations, while highlighting the effects of modal energy transfer and internal resonances. A multiphysics coupled model of the beam-piezoelectric system is proposed based on the nonlinear beam theory of Bernoulli–Euler and the piezoelectric constitutive equations. The discretized model of the system is obtained with the help of the Galerkin weighted residual technique while retaining 32 degrees-of-freedom. Three-dimensional finite element analysis is conducted as well in the static regime to validate the developed model and numerical simulation. It is shown that the response of the system in the nonlinear resonant region is strongly affected by a three-to-one internal resonance.

Dynamic Finite Element Analysis of a Highly Parallel Robotic Surface

2011 ◽  
Author(s):  
Chris Salisbury
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Angular Displacement ◽  
Three Dimensional ◽  
Element Analysis ◽  
Revolute Joints ◽  
Stiffness Matrices ◽  
Joint Forces ◽  
Ricatti Equation ◽  
Optimal Dynamic

A novel three-dimensional robotic surface is devised using triangular modules connected by revolute joints that mimic the constraints of a spherical joint at each triangle intersection. The finite element method (FEM) is applied to the dynamic loading of this device using three dimensional (6 degrees of freedom) beam elements to not only calculate the cartesian displacement and force, but also the angular displacement and torque at each joint. In this way, the traditional methods of finding joint forces and torques are completely bypassed. An effiecient algorithm is developed to linearly combine local mass and stiffness matrices into a full structural stiffness matrix for the easy application of loads. An analysis of optimal dynamic joint forces is carried out in Simulink® with the use of an algebraic Ricatti equation.

Three-Dimensional Creep Analysis of Solder Joints in Surface Mount Devices

1995 ◽  
Vol 117 (1) ◽  
pp. 20-25 ◽  
Author(s):  
Pardeep K. Bhatti ◽  
Klaus Gschwend ◽  
Abel Y. Kwang ◽  
Ahmer R. Syed
Keyword(s):  
High Performance ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Nonlinear Material ◽  
Computational Time ◽  
Nonlinear Creep ◽  
Element Analysis ◽  
Surface Mount ◽  
Creep Analysis ◽  
Highly Nonlinear

Three-dimensional finite element analysis has been applied for determining time-dependent solder joint response of leaded surface mount components under thermal cycling. Two main challenges are the geometric complexity in mesh development and computationally intensive analysis because of the highly nonlinear material properties. Advanced techniques have been applied, including multi-point constraints for mesh transition, which reduces the number of degrees of freedom in the model, and substructuring, which effectively reduces computational time in the iterative analysis. The result is a generic approach for nonlinear creep analysis using commercial FEA software on a high performance workstation. Illustrations are provided for J and gullwing leaded packages.

Three-dimensional vibration of a ring with a noncircular cross-section on an elastic foundation

2017 ◽  
Vol 232 (13) ◽  
pp. 2381-2393 ◽  
Author(s):  
Zhe Liu ◽  
Fuqiang Zhou ◽  
Christian Oertel ◽  
Yintao Wei
Keyword(s):  
Elastic Foundation ◽  
Cross Section ◽  
Three Dimensional ◽  
Theoretical Formula ◽  
Variation Principle ◽  
Displacement Fields ◽  
Element Analysis ◽  
Noncircular Cross Section ◽  
Truck Tire ◽  
Out Of Plane

The three-dimensional dynamic equations of a ring with a noncircular cross-section on an elastic foundation are obtained using the Hamilton variation principle. In contrast to the previous rings on elastic foundation model, the developed model incorporates both the in-plane and out-of-plane bend and the out-of-plane torsion in displacement fields. The errors in the derivation of the initial stress and the work of the internal pressure in previous rings on elastic foundation models have been corrected. The mode expansion was used to obtain the analytical solution of the natural frequency. The initial motivation is to develop a theoretical model for car tire dynamics. Therefore, to validate the proposed model, the in-plane and out-of-plane vibrations of a truck tire have been analyzed using the proposed method. To further verify the accuracy of the model, the results of the theoretical formula are compared with the finite element analysis and modal test, and good agreement can be found.

A novel direct resolution method for coupled systems in finite element analysis

2020 ◽  
Vol 39 (5) ◽  
pp. 1271-1280
Author(s):  
Youcef Boutora ◽  
Noureddine Takorabet
Keyword(s):  
Finite Elements ◽  
Linear Systems ◽  
Symmetric Matrix ◽  
Direct Method ◽  
Three Dimensional ◽  
Coupled Systems ◽  
Resolution Method ◽  
Element Analysis ◽  
Content Type ◽  
Magnetostatic Problem

Purpose This paper aims to propose a novel direct method for indefinite algebraic linear systems. It is well adapted for sparse linear systems, such as those of two-dimensional (2-D) finite elements problems, especially for coupled systems. Design/methodology/approach The proposed method is developed on an example of an indefinite symmetric matrix. The algorithm of the method is given next, and a comparison between the numbers of operations required by the method and the Cholesky method is also given. Finally, an application on a magnetostatic problem for classical methods (Gauss and Cholesky) shows the relative efficiency of the proposed method. Findings The proposed method can be used advantageously for 2-D finite elements in stepping methods without using a block decomposition of matrices. Research limitations/implications This method is advantageous for direct linear solving for 2-D problems, but it is not recommended at this time for three-dimensional problems. Originality/value The proposed method is the first direct solver for algebraic linear systems proposed since more than a half century. It is not limited for symmetric positive systems such as many of direct and iterative methods.

Elastic-Plastic Finite Element Simulation of Bulge Forming Process Using a Variable Cross-Section Solid Bulging Mold

2011 ◽  
Vol 189-193 ◽  
pp. 4405-4408
Author(s):  
Ke Wang ◽  
Zhe Ying Wang ◽  
Xing Wei Sun
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Metal Flow ◽  
Three Dimensional ◽  
Variable Cross Section ◽  
Flow Mode ◽  
Variable Cross ◽  
Forming Process ◽  
Element Analysis ◽  
Screw Rotor

Bulge forming is a novel process aimed at common products including T-branches, cross branches and angle branches. But bulging forming has not applied for two-head abnormity-shaped hollow screw rotor reported in literature. Simulation of the bulging forming of two-head abnormity-shaped hollow screw rotor has not been reported. This paper presents a simulation of the bulge forming process of two-head abnormity-shaped hollow screw rotor using a variable cross-section solid bulging mold. Some conditions including the effect of friction, boundary conditions, contact conditions and the space motion, etc are presented. The mathematical model of three-dimensional finite element analysis has been established. The distribution of generalized plastic strain and general metal flow mode in cross section of two abnormity-shaped hollow screw rotor has been analyzed. It is an effective method for the analysis of other defects and the optimization of process parameters further.

A Four-Node Tetrahedral Finite Element Based on Space Fiber Rotation Concept

2019 ◽  
Vol 11 (1) ◽  
pp. 67-78
Author(s):  
Kamel Meftah ◽  
Lakhdar Sedira
Keyword(s):  
Finite Element ◽  
Strain Field ◽  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Field Tensor ◽  
Tetrahedral Element ◽  
Numerical Studies ◽  
Rotational Degrees Of Freedom ◽  
Tensor Approximation

Abstract The paper presents a four-node tetrahedral solid finite element SFR4 with rotational degrees of freedom (DOFs) based on the Space Fiber Rotation (SFR) concept for modeling three-dimensional solid structures. This SFR concept is based on the idea that a 3D virtual fiber, after a spatial rotation, introduces an enhancement of the strain field tensor approximation. Full numerical integration is used to evaluate the element stiffness matrix. To demonstrate the efficiency and accuracy of the developed four-node tetrahedron solid element and to compare its performance with the classical four-node tetrahedral element, extensive numerical studies are presented.

Finite Element Analysis of Coupled Lateral and Torsional Vibrations of a Rotor With Multiple Cracks

2005 ◽  
Author(s):  
Xi Wu ◽  
Jerzy T. Sawicki ◽  
Michael I. Friswell ◽  
George Y. Baaklini
Keyword(s):  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Accurate Determination ◽  
Crack Model ◽  
Multiple Cracks ◽  
Torsional Vibrations ◽  
Element Analysis ◽  
Cosine Series ◽  
Six Degrees Of Freedom ◽  
Stiffness Matrices

The coupling between lateral and torsional vibrations has been investigated for a rotor dynamic system with breathing crack model. The stiffness matrix has been developed for the shaft element which accounts for the effect of the crack and all six degrees of freedom per node. Since the off-diagonal terms of the stiffness matrix represent the coupling of the respective modes, the special attention has been paid on accurate determination of their values. Based on the concepts of fracture mechanics, the variation of the stiffness matrix over the full shaft revolution is represented by the truncated cosine series where the fitting coefficient matrices are extracted from the stiffness matrices of the cracked shaft for a number of its different angular positions. The variation of the system eigenfrequencies and dynamic response of the rotor with two cracks have been studied for various shaft geometries, crack axial locations, and relative phase of cracks.

Finite Element Analysis on Dynamic Characteristics of Maglev Suspension System

2013 ◽  
Vol 834-836 ◽  
pp. 1497-1500
Author(s):  
Jian Xiang Tang ◽  
Xin Hua Jiang ◽  
Jiang Min Deng ◽  
Te Fang Chen
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Dynamic Characteristics ◽  
High Performance ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Suspension System ◽  
Three Dimensional Model ◽  
Maglev Train ◽  
Element Analysis

In this paper, electromagnetic dynamic characteristics of suspension system of middle-low speed maglev train are analyzed with finite element analysis (FEA) method based on the high-performance computing platform (HPC). The couple structure between F-type track and suspension magnet is meshed by pretension element. The dynamic characteristics of suspension system are simulated in three-dimensional model with 4 degrees of freedom motions condition. Both the numerical simulations and the actual force tests of suspension system are carried out with the same input. The result shows that the calculation accuracy of finite element analysis is high.

The biomechanical study of cervical spine: A Finite Element Analysis

2021 ◽  
pp. 039139882199549
Author(s):  
Pechimuthu Susai Manickam ◽  
Sandipan Roy
Keyword(s):  
Finite Element ◽  
Cervical Spine ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Biomechanical Study ◽  
Fe Analysis ◽  
Von Mises Stress ◽  
Fe Model ◽  
Element Analysis ◽  
End Plate

The biomechanical study helps us to understand the mechanics of the human cervical spine. A three dimensional Finite Element (FE) model for C3 to C6 level was developed using computed tomography (CT) scan data to study the mechanical behaviour of the cervical spine. A moment of 1 Nm was applied at the top of C3 vertebral end plate and all degrees of freedom of bottom end plate of C6 were constrained. The physiological motion of the cervical spine was validated using published experimental and FE analysis results. The von Mises stress distribution across the intervertebral disc was calculated along with range of motion. It was observed that the predicted results of functional spine units using FE analysis replicate the real behaviour of the cervical spine.

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