Nonlinear Deformation and Numerical Post-Buckling Analysis of Plate Structures Using the Assumed Natural Strain Concept

2021 ◽  
Author(s):  
Mohammad Rezaiee-Pajand ◽  
Mohammadreza Ramezani
Keyword(s):  
Degrees Of Freedom ◽  
High Efficiency ◽  
Variational Calculus ◽  
Triangular Element ◽  
Plate Structures ◽  
Natural Strain ◽  
Total Potential ◽  
Post Buckling ◽  
Assumed Natural Strain ◽  
Updated Lagrangian

In this study, an efficient triangular element for the fast nonlinear analysis of moderately thick Mindlin–Reissner plates is proposed. The element is formulated using a newly developed method, which is based on the assumed natural strain concept, and called Continuously Variable Strain (CVS). The continuous higher-order strain field is proposed by using the fundamental lemma of the variational calculus. Furthermore, the updated Lagrangian tensor together with rigid body terms is employed allowing for large deformations. The proposed element (CVST10), which is obtained by minimizing the total potential energy, has only 10 degrees of freedom and demonstrates high-efficiency and fast convergence rate in analysis of problems with coarse and distorted meshes. The arc-length iterative technique is applied to handle the geometrically post-buckling behavior of homogeneous plates under various load and boundary conditions. Various numerical examples prove the accuracy of the proposed element.

scholarly journals A Conforming Triangular Plane Element with Rotational Degrees of Freedom

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Xiang-Rong Fu ◽  
Ming-Wu Yuan ◽  
Chen Pu
Keyword(s):  
Isotropic Material ◽  
Degrees Of Freedom ◽  
High Efficiency ◽  
High Accuracy ◽  
Triangular Element ◽  
Linear Distribution ◽  
Rotational Displacement ◽  
Plane Element ◽  
Rotational Degrees Of Freedom ◽  
Integral Formulae

This paper presents a novel way to formulate the triangular plane element with rotational degrees of freedom (RDOF). The linear distribution of rotational displacement is assumed. The conforming displacement along the sides based on the rotational displacement assumption is derived, and the triangular plane element TR3 for isotropic material is formulated. By using the explicit integral formulae of the triangular element, the matrices used in the proposed plane element TR3 are calculated efficiently. The benchmark examples showed thier high accuracy and high efficiency.

A Two-Dimensional Linear Assumed Strain Triangular Element for Finite Deformation Analysis

2005 ◽  
Vol 73 (6) ◽  
pp. 970-976 ◽  
Author(s):  
Fernando G. Flores
Keyword(s):  
Finite Deformation ◽  
Degrees Of Freedom ◽  
Yield Function ◽  
Triangular Element ◽  
Deformation Analysis ◽  
Elastic Model ◽  
Stress Strain ◽  
Metric Tensor ◽  
Assumed Strain ◽  
Non Linear

An assumed strain approach for a linear triangular element able to handle finite deformation problems is presented in this paper. The element is based on a total Lagrangian formulation and its geometry is defined by three nodes with only translational degrees of freedom. The strains are computed from the metric tensor, which is interpolated linearly from the values obtained at the mid-side points of the element. The evaluation of the gradient at each side of the triangle is made resorting to the geometry of the adjacent elements, leading to a four element patch. The approach is then nonconforming, nevertheless the element passes the patch test. To deal with plasticity at finite deformations a logarithmic stress-strain pair is used where an additive decomposition of elastic and plastic strains is adopted. A hyper-elastic model for the elastic linear stress-strain relation and an isotropic quadratic yield function (Mises) for the plastic part are considered. The element has been implemented in two finite element codes: an implicit static/dynamic program for moderately non-linear problems and an explicit dynamic code for problems with strong nonlinearities. Several examples are shown to assess the behavior of the present element in linear plane stress states and non-linear plane strain states as well as in axi-symmetric problems.

A Hybrid Highly Parallelizable Algorithm for the Dynamics of Rigid Body Chain Systems

1999 ◽  
Author(s):  
Shanzhong Duan ◽  
Kurt S. Anderson
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
High Efficiency ◽  
Equations Of Motion ◽  
Constraint Forces ◽  
Dynamics Of Rigid Body ◽  
A Chain ◽  
Explicit Determination ◽  
Order Algorithm

Abstract The paper presents a new hybrid parallelizable low order algorithm for modeling the dynamic behavior of multi-rigid-body chain systems. The method is based on cutting certain system interbody joints so that largely independent multibody subchain systems are formed. These subchains interact with one another through associated unknown constraint forces f¯c at the cut joints. The increased parallelism is obtainable through cutting the joints and the explicit determination of associated constraint loads combined with a sequential O(n) procedure. In other words, sequential O(n) procedures are performed to form and solve equations of motion within subchains and parallel strategies are used to form and solve constraint equations between subchains in parallel. The algorithm can easily accommodate the available number of processors while maintaining high efficiency. An O[(n+m)Np+m(1+γ)Np+mγlog2Np](0<γ<1) performance will be achieved with Np processors for a chain system with n degrees of freedom and m constraints due to cutting of interbody joints.

Development of six-DOF welding robot with machine vision

2018 ◽  
Vol 32 (34n36) ◽  
pp. 1840079
Author(s):  
Wensheng Huang ◽  
Hongli Xu
Keyword(s):  
Machine Vision ◽  
High Speed ◽  
Degrees Of Freedom ◽  
High Efficiency ◽  
Target Location ◽  
Industrial Robots ◽  
Welding Robot ◽  
Edge Pixel ◽  
Six Dof ◽  
Hardware Processing

The application of machine vision to industrial robots is a hot topic in robot research nowadays. A welding robot with machine vision had been developed, which is convenient and flexible to reach the welding point with six degrees-of-freedom (DOF) manipulator, while the singularity of its movement trail is prevented, and the stability of the mechanism had been fully guaranteed. As the precise industry camera can capture the optical feature of the workpiece to reflect in the camera’s CCD lens, the workpiece is identified and located through a visual pattern recognition algorithm based on gray scale processing, on the gradient direction of edge pixel or on geometric element so that high-speed visual acquisition, image preprocessing, feature extraction and recognition, target location are integrated and hardware processing power is improved. Another task is to plan control strategy of control system, and the upper computer software is programmed in order that multi-axis motion trajectory is optimized and servo control is accomplished. Finally, prototype was developed and validation experiments show that the welding robot has high stability, high efficiency, high precision, even if welding joints are random and workpiece contour is irregular.

scholarly journals Recent Design Optimization Methods for Energy-Efficient Electric Motors and Derived Requirements for a New Improved Method—Part 1

Proceedings ◽  
2018 ◽  
Vol 2 (22) ◽  
pp. 1400
Author(s):  
Johannes Schmelcher ◽  
Max Kleine Büning ◽  
Kai Kreisköther ◽  
Dieter Gerling ◽  
Achim Kampker
Keyword(s):  
Rare Earth ◽  
Design Optimization ◽  
Energy Efficient ◽  
Degrees Of Freedom ◽  
High Efficiency ◽  
Optimization Problems ◽  
Computing Time ◽  
Optimization Methods ◽  
Electric Motors ◽  
Electric Cars

Energy-efficient electric motors are gathering an increased attention since they are used in electric cars or to reduce operational costs, for instance. Due to their high efficiency, permanent-magnet synchronous motors are used progressively more. However, the need to use rare-earth magnets for such high-efficiency motors is problematic not only in regard to the cost but also in socio-political and environmental aspects. Therefore, an increasing effort has to be put in finding the best design possible. The goals to achieve are, among others, to reduce the amount of rare-earth magnet material but also to increase the efficiency. In the first part of this multipart paper, characteristics of optimization problems in engineering and general methods to solve them are presented. In part two, different approaches to the design optimization problem of electric motors are highlighted. The last part will evaluate the different categories of optimization methods with respect to the criteria: degrees of freedom, computing time and the required user experience. As will be seen, there is a conflict of objectives regarding the criteria mentioned above. Requirements, which a new optimization method has to fulfil in order to solve the conflict of objectives will be presented in this last paper.

Finite Element Analysis of 2-D Structures by New Strain Based Triangular Element

2018 ◽  
Vol 35 (3) ◽  
pp. 305-313 ◽  
Author(s):  
C. Rebiai
Keyword(s):  
Dynamic Analysis ◽  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
Time Integration ◽  
Triangular Element ◽  
Membrane Element ◽  
Lumped Mass ◽  
Element Analysis ◽  
Benchmark Tests ◽  
Three Degrees Of Freedom

ABSTRACTIn this investigation, a new simple triangular strain based membrane element with drilling rotation for 2-D structures analysis is proposed. This new numerical model can be used for linear and dynamic analysis. The triangular element is named SBTE and it has three nodes with three degrees of freedom at each node. The displacements field of this element is based on the assumed functions for the various strains satisfying the compatibility equations. This developed element passed both patch and benchmark tests in the case of bending and shear problems. For the dynamic analysis, lumped mass with implicit/explicit time integration are employed. The obtained numerical results using the developed element converge toward the analytical and numerical solutions in both analyses.

scholarly journals Quaternionic wave function

2019 ◽  
Vol 34 (02) ◽  
pp. 1950001 ◽  
Author(s):  
Pavel A. Bolokhov
Keyword(s):  
Wave Function ◽  
Quantum Electrodynamics ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Variational Calculus ◽  
Nonrelativistic Limit ◽  
Natural Choice ◽  
Complex Wave ◽  
Spinor Formalism ◽  
Function Language

We argue that quaternions form a natural language for the description of quantum-mechanical wave functions with spin. We use the quaternionic spinor formalism which is in one-to-one correspondence with the usual spinor language. No unphysical degrees of freedom are admitted, in contrast to the majority of literature on quaternions. In this paper, we first build a Dirac Lagrangian in the quaternionic form, derive the Dirac equation and take the nonrelativistic limit to find the Schrödinger’s equation. We show that the quaternionic formalism is a natural choice to start with, while in the transition to the noninteracting nonrelativistic limit, the quaternionic description effectively reduces to the regular complex wave function language. We provide an easy-to-use grammar for switching between the ordinary spinor language and the description in terms of quaternions. As an illustration of the broader range of the formalism, we also derive the Maxwell’s equation from the quaternionic Lagrangian of Quantum Electrodynamics. In order to derive the equations of motion, we develop the variational calculus appropriate for this formalism.

A Hybrid Analytical and Finite Element Method for Mid-Frequency Vibration Analysis of Plate Structures with Discontinuities

2017 ◽  
Vol 17 (04) ◽  
pp. 1750052 ◽  
Author(s):  
Yongbin Ma ◽  
Yahui Zhang ◽  
Bo Ping Wang
Keyword(s):  
Finite Element ◽  
Vibration Analysis ◽  
Present Method ◽  
High Efficiency ◽  
Main Idea ◽  
High Accuracy ◽  
Symplectic Method ◽  
Rectangular Plates ◽  
Fe Method ◽  
Plate Structures

A hybrid analytical and numerical method is presented for the mid-frequency vibration analysis of a class of plate structures with discontinuities based on the concept of structural partitioning. The type of structures considered includes rectangular plates with internal property discontinuity, homogeneous but non-rectangular plates, or built-up structures composed of rectangular homogenous plates with complex joints. Compared with the conventional finite element (FE) method, the present method has the advantage of high accuracy and high efficiency in the analysis of mid-frequency vibration of the structures of concern. The main idea of the proposed approach is to divide the whole structure into uniform rectangular plate regions and other non-rectangular regions. The vibration behavior of the rectangular regions is accurately and efficiently described by analytical wave solutions so that the FE modeling for these regions is not necessary. The other non-rectangular regions are modeled by the conventional FE method. The analytical waves used to describe the rectangular regions are obtained by the symplectic method, thereby avoiding the limitation of the conventional analytical method in dealing with plates having two opposite edges simply supported. By enforcing the displacement continuity and force equilibrium at the connection interfaces, the dynamic coupling is established between the rectangular regions described in terms of the analytical waves and the regions modeled by FEs. Furthermore, the hybrid solution formulation for the mid-frequency vibration of the entire structure is proposed. The high accuracy and efficiency of the present method are demonstrated by several numerical examples, with the effect of element size of the FE regions investigated. Finally, the applicability of the proposed method is analyzed.

scholarly journals Finite Element Vibration Analysis of Laminated Composite Folded Plate Structures

1999 ◽  
Vol 6 (5-6) ◽  
pp. 273-283 ◽  
Author(s):  
A. Guha Niyogi ◽  
M.K. Laha ◽  
P.K. Sinha
Keyword(s):  
Finite Element ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Laminated Composite ◽  
Mode Shapes ◽  
Plate Structures ◽  
Drilling Degree Of Freedom ◽  
Vibration Responses ◽  
Forced Vibration Analysis

A nine-noded Lagrangian plate bending finite element that incorporates first-order transverse shear deformation and rotary inertia is used to predict the free and forced vibration response of laminated composite folded plate structures. A 6 × 6 transformation matrix is derived to transform the system element matrices before assembly. The usual five degrees-of-freedom per node is appended with an additional drilling degree of freedom in order to fit the transformation. The present finite element results show good agreement with the available semi-analytical solutions and finite element results. Parametric studies are conducted for free and forced vibration analysis for laminated folded plates, with reference to crank angle, fibre angle and stacking sequence. The natural frequencies and mode shapes, and forced vibration responses furnished here may serve as a benchmark for future investigations.

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