scholarly journals A modified four-node rectangular element

2019 ◽  
Vol 52 (3) ◽  
pp. 192-199
Author(s):  
Jouni Freund ◽  
Eero-Matti Salonen
Keyword(s):  
Stiffness Matrix ◽  
Strain Energy ◽  
Virtual Work ◽  
Shear Behavior ◽  
Single Element ◽  
Principle Of Virtual Work ◽  
Bending Mode ◽  
Incompatible Modes ◽  
Rectangular Element ◽  
Parameter Values

The sensitized principle of virtual work is applied to modify the stiffness matrix of the ordinary four-node rectangular element by sensitizing terms. The sensitizing parameter values are determined by the single-element strain energy test. The reference solutions used are of bending mode types and their application removes the so-called parasitic shear behavior. A stiffness matrix of good quality is obtained corresponding exactly to an earlier formulation using incompatible modes.

Kinematic, Stiffness, and Dynamic Analyses of a Compliant Tensegrity Mechanism

2014 ◽  
Vol 6 (4) ◽  
Author(s):  
Bahman Nouri Rahmat Abadi ◽  
S. M. Mehdi Shekarforoush ◽  
Mojtaba Mahzoon ◽  
Mehrdad Farid
Keyword(s):  
Dynamic Characteristics ◽  
Stiffness Matrix ◽  
Analytical Procedure ◽  
Inverse Dynamics ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Degree Of Freedom ◽  
Principle Of Virtual Work ◽  
Numerical Examples ◽  
Dynamic Analyses

The objective of this study is to present an analytical procedure for analysis of a compliant tensegrity mechanism focusing on its stiffness and dynamic characteristics. The screw calculus is used to derive the static equations and stiffness matrix of a full degree-of-freedom tensegrity mechanism, and the equations of motion are derived based on the principle of virtual work. Finally, some numerical examples are solved for the inverse dynamics of the mechanism.

On the Mechanical Behavior of the Orthotropic Cord-Rubber Composite

1976 ◽  
Vol 4 (4) ◽  
pp. 219-232 ◽  
Author(s):  
Ö. Pósfalvi
Keyword(s):  
Mechanical Behavior ◽  
Uniaxial Tension ◽  
Elastic Properties ◽  
Large Deformations ◽  
Virtual Work ◽  
Poisson's Ratio ◽  
Principle Of Virtual Work ◽  
Effective Elastic Properties ◽  
Rubber Composite ◽  
Mooney Equation

Abstract The effective elastic properties of the cord-rubber composite are deduced from the principle of virtual work. Such a composite must be compliant in the noncord directions and therefore undergo large deformations. The Rivlin-Mooney equation is used to derive the effective Poisson's ratio and Young's modulus of the composite and as a basis for their measurement in uniaxial tension.

scholarly journals Discrete element model for general polyhedra

2021 ◽  
Author(s):  
Alfredo Gay Neto ◽  
Peter Wriggers
Keyword(s):  
Frictional Contact ◽  
Virtual Work ◽  
Particle Surface ◽  
Element Model ◽  
Discrete Element ◽  
Discrete Element Model ◽  
Principle Of Virtual Work ◽  
Dynamics Model ◽  
Railway Ballast ◽  
Multibody Dynamics Model

AbstractWe present a version of the Discrete Element Method considering the particles as rigid polyhedra. The Principle of Virtual Work is employed as basis for a multibody dynamics model. Each particle surface is split into sub-regions, which are tracked for contact with other sub-regions of neighboring particles. Contact interactions are modeled pointwise, considering vertex-face, edge-edge, vertex-edge and vertex-vertex interactions. General polyhedra with triangular faces are considered as particles, permitting multiple pointwise interactions which are automatically detected along the model evolution. We propose a combined interface law composed of a penalty and a barrier approach, to fulfill the contact constraints. Numerical examples demonstrate that the model can handle normal and frictional contact effects in a robust manner. These include simulations of convex and non-convex particles, showing the potential of applicability to materials with complex shaped particles such as sand and railway ballast.

Consistent co-rotational framework for Euler-Bernoulli and Timoshenko beam-column elements under distributed member loads

2021 ◽  
pp. 136943322098663
Author(s):  
Yi-Qun Tang ◽  
Wen-Feng Chen ◽  
Yao-Peng Liu ◽  
Siu-Lai Chan
Keyword(s):  
Coordinate System ◽  
Stiffness Matrix ◽  
Traditional Method ◽  
Local Coordinate System ◽  
Frame Structures ◽  
Global Coordinate System ◽  
Single Element ◽  
Geometrically Nonlinear ◽  
Geometrically Nonlinear Analysis ◽  
Geometric Stiffness

Conventional co-rotational formulations for geometrically nonlinear analysis are based on the assumption that the finite element is only subjected to nodal loads and as a result, they are not accurate for the elements under distributed member loads. The magnitude and direction of member loads are treated as constant in the global coordinate system, but they are essentially varying in the local coordinate system for the element undergoing a large rigid body rotation, leading to the change of nodal moments at element ends. Thus, there is a need to improve the co-rotational formulations to allow for the effect. This paper proposes a new consistent co-rotational formulation for both Euler-Bernoulli and Timoshenko two-dimensional beam-column elements subjected to distributed member loads. It is found that the equivalent nodal moments are affected by the element geometric change and consequently contribute to a part of geometric stiffness matrix. From this study, the results of both eigenvalue buckling and second-order direct analyses will be significantly improved. Several examples are used to verify the proposed formulation with comparison of the traditional method, which demonstrate the accuracy and reliability of the proposed method in buckling analysis of frame structures under distributed member loads using a single element per member.

Analytical Modelling of the Dynamics of the Four-Bar Mechanism: A Comparison of Some Methods

2018 ◽  
Author(s):  
J. P. Meijaard ◽  
V. van der Wijk
Keyword(s):  
Virtual Work ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Force Balance ◽  
Dynamic Force ◽  
Algebraic Equations ◽  
Principle Of Virtual Work ◽  
Principal Vector ◽  
Reaction Forces ◽  
Principal Points

Some thoughts about different ways of formulating the equations of motion of a four-bar mechanism are communicated. Four analytic methods to derive the equations of motion are compared. In the first method, Lagrange’s equations in the traditional form are used, and in a second method, the principle of virtual work is used, which leads to equivalent equations. In the third method, the loop is opened, principal points and a principal vector linkage are introduced, and the equations are formulated in terms of these principal vectors, which leads, with the introduced reaction forces, to a system of differential-algebraic equations. In the fourth method, equivalent masses are introduced, which leads to a simpler system of principal points and principal vectors. By considering the links as pseudorigid bodies that can have a uniform planar dilatation, a compact form of the equations of motion is obtained. The conditions for dynamic force balance become almost trivial. Also the equations for the resulting reaction moment are considered for all four methods.

Static analysis of spatial parallel manipulators by means of the principle of virtual work

2012 ◽  
Vol 28 (3) ◽  
pp. 385-401 ◽  
Author(s):  
J. Jesús Cervantes-Sánchez ◽  
José M. Rico-Martínez ◽  
Salvador Pacheco-Gutiérrez ◽  
Gustavo Cerda-Villafaña
Keyword(s):  
Static Analysis ◽  
Virtual Work ◽  
Parallel Manipulators ◽  
Principle Of Virtual Work

Geometrical Stiffness of Thin-Walled I-Beam Element Based on Rigid-Beam Assemblage Concept

2012 ◽  
Vol 28 (1) ◽  
pp. 97-106 ◽  
Author(s):  
J. D. Yau ◽  
S.-R. Kuo
Keyword(s):  
Stiffness Matrix ◽  
Virtual Work ◽  
Bending Moment ◽  
Beam Element ◽  
Narrow Beam ◽  
Cross Sectional ◽  
Geometric Stiffness ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Thin Walled

ABSTRACTUsing conventional virtual work method to derive geometric stiffness of a thin-walled beam element, researchers usually have to deal with nonlinear strains with high order terms and the induced moments caused by cross sectional stress results under rotations. To simplify the laborious procedure, this study decomposes an I-beam element into three narrow beam components in conjunction with geometrical hypothesis of rigid cross section. Then let us adopt Yanget al.'s simplified geometric stiffness matrix [kg]12×12of a rigid beam element as the basis of geometric stiffness of a narrow beam element. Finally, we can use rigid beam assemblage and stiffness transformation procedure to derivate the geometric stiffness matrix [kg]14×14of an I-beam element, in which two nodal warping deformations are included. From the derived [kg]14×14matrix, it can take into account the nature of various rotational moments, such as semi-tangential (ST) property for St. Venant torque and quasi-tangential (QT) property for both bending moment and warping torque. The applicability of the proposed [kg]14×14matrix to buckling problem and geometric nonlinear analysis of loaded I-shaped beam structures will be verified and compared with the results presented in existing literatures. Moreover, the post-buckling behavior of a centrally-load web-tapered I-beam with warping restraints will be investigated as well.

Optimal Design of Bi- and Multi-Stable Compliant Cellular Structures

2018 ◽  
Author(s):  
Quantian Luo ◽  
Liyong Tong
Keyword(s):  
Optimal Design ◽  
Virtual Work ◽  
Reaction Force ◽  
Nonlinear Finite Element ◽  
Cellular Structures ◽  
Stress And Strain ◽  
Principle Of Virtual Work ◽  
Stable States ◽  
Threshold Method ◽  
Element Analysis

This paper presents optimal design for nonlinear compliant cellular structures with bi- and multi-stable states via topology optimization. Based on the principle of virtual work, formulations for displacements and forces are derived and expressed in terms of stress and strain in all load steps in nonlinear finite element analysis. Optimization for compliant structures with bi-stable states is then formulated as: 1) to maximize the displacement under specified force larger than its critical one; and 2) to minimize the reaction force for the prescribed displacement larger than its critical one. Algorithms are developed using the present formulations and the moving iso-surface threshold method. Optimal design for a unit cell with bi-stable states is studied first, and then designs of multi-stable compliant cellular structures are discussed.

On the Sufficiency of the Principle of Virtual Work for Mechanical Equilibrium: A Critical Reexamination

1989 ◽  
Vol 56 (3) ◽  
pp. 704-707 ◽  
Author(s):  
John G. Papastavridis
Keyword(s):  
Virtual Work ◽  
Mechanical Equilibrium ◽  
Principle Of Virtual Work ◽  
Holonomic Constraints ◽  
Kinetic Principle ◽  
Sufficiency Conditions

Starting from the general kinetic principle of d’Alembert/Lagrange, an energetic proof of the sufficiency conditions for equilibrium (known as Principle of Virtual Work) is presented. It is clearly demonstrated why to maintain equilibrium requires that, in addition to the familiar vanishing of the virtual work of the impressed forces on the originally motionless system, its geometrical (holonomic) constraints be explicitly time independent (stationary) and its nonintegrable kinematical (nonholonomic) ones be linear and homogeneous in the generalized velocities (catastatic).

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