Size effect in piezoelectric semiconductor nanostructures

A gradient theory is applied to the mechanical constitutive equations for piezoelectric semiconductor nanostructures. This is achieved by considering the strain gradients in the constitutive equation with high-order stresses and electric displacements in advanced continuum model. The C1 continuous interpolations of displacements or a mixed formulation is required in the finite element method (FEM) due to the presence of the second-order derivative on the elastic displacements. A mixed FEM is then developed from the principle of virtual work. Numerical examples clearly show the significant effect of flexoelectricity on the induced electric potential and electric current in the piezoelectric semiconductor nanostructures.

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Dynamic Analysis of Spatial Four-Degree-of-Freedom Parallel Manipulators

Volume 2: 23rd Design Automation Conference ◽

10.1115/detc97/dac-3759 ◽

1997 ◽

Author(s):

Jiegao Wang ◽

Clément M. Gosselin

Keyword(s):

Dynamic Analysis ◽

Virtual Work ◽

Parallel Manipulators ◽

Degree Of Freedom ◽

Principle Of Virtual Work ◽

Numerical Examples ◽

Euler Approach

Abstract The dynamic analysis of spatial four-degree-of-freedom parallel manipulators is presented in this article. First, expressions for the position, velocity and acceleration of each link constituting the manipulators are obtained. Then, the principle of virtual work is used to derive the generalized input forces of the manipulators. The corresponding algorithm is implemented and numerical examples are given in order to illustrate the results. The results obtained are verified using the classical Newton-Euler approach.

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ОСНОВНЫЕ УРАВНЕНИЯ, ГРАНИЧНЫЕ УСЛОВИЯ И ВАРИАЦИОННЫЙ ПРИНЦИП ПЛОСКОЙ ЗАДАЧИ ГРАДИЕНТНОЙ ТЕОРИИ УПРУГОСТИ ДЛЯ ПРЯМОУГОЛЬНОЙ ОБЛАСТИ / BASIC EQUATIONS, BOUNDARY CONDITIONS AND VARIATION PRINCIPLES OF THE PLANE PROBLEM IN THE GRADIENT THEORY OF ELASTICITY FOR A RECTANGULAR DOMAIN

SUSh Scientific Proceedings ◽

10.54151/27382559-2021.1a-20 ◽

2021 ◽

pp. 20-28

Author(s):

L. Sargsyan

Keyword(s):

Boundary Conditions ◽

Plane Problem ◽

Virtual Work ◽

Gradient Elasticity ◽

Theory Of Elasticity ◽

Rectangular Domain ◽

Gradient Theory ◽

Principle Of Virtual Work ◽

Balance Equations ◽

Basic Equations

В работе приведены основные уравнения плоской задачи градиентной теории упругости для прямоугольной области и устанавливается принцип возможных перемещений с соответствующем вариационном уравнением. Из вариационного уравнения теории упругости и для прямоугольной области все граничные условия. / The paper demonstrates the basic equations of the plane problem in the frames of the theory of gradient elasticity and establishes the principle of virtual work along with its variation equations. The basic balance equations of the plane problem of the theory of gradient elasticity and the boundary conditions for the rectangular plane are derived.

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Basic Equations of Dynamic Elastic Stability for Thin-Walled Structural Members Subjected to Follower Loads and Their Application to Non-Conservative Torque Problems

Transactions of the Canadian Society for Mechanical Engineering ◽

10.1139/tcsme-1985-0011 ◽

1985 ◽

Vol 9 (2) ◽

pp. 75-83 ◽

Cited By ~ 3

Author(s):

Tadayoshi Aida

Keyword(s):

Virtual Work ◽

Elastic Stability ◽

Structural Members ◽

Principle Of Virtual Work ◽

Torsional Moment ◽

Channel Section ◽

Numerical Examples ◽

Thin Walled ◽

Basic Equations ◽

The Stability

The basic equations and the boundary conditions, in which the effect of an initial torsional moment Mz0 is included, and needed for the analysis of the dynamic elastic stability of thin-walled structural members subjected to follower loads are derived by introducing the concept of initial stress and using the principle of virtual work. The stability problems of columns with a channel section subjected to a non-conservative torque are investigated in terms of numerical examples.

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Effect of Coiled Tubing Initial Configuration on Buckling Behavior in Deviated Wells

Journal of Energy Resources Technology ◽

10.1115/1.2795979 ◽

1999 ◽

Vol 121 (3) ◽

pp. 176-182 ◽

Cited By ~ 1

Author(s):

W. Y. Qiu ◽

S. Z. Miska ◽

L. J. Volk

Keyword(s):

Virtual Work ◽

Initial Configuration ◽

Initial Amplitude ◽

Principle Of Virtual Work ◽

Conservation Of Energy ◽

Numerical Examples ◽

Coiled Tubing ◽

Buckling Behavior ◽

Helical Buckling ◽

Deviated Wells

Current sinusoidal and helical buckling models are valid only for initially straight coiled tubing (CT). This paper stresses the effect of the pipe initial configuration (residual bending) on the sinusoidal and helical buckling behaviors in deviated wells. Using the conservation of energy and the principle of virtual work, new general equations are derived for predicting the sinusoidal and helical configurations of CT. These new equations reduce to those previously published when the CT is initially straight in deviated wells. Numerical examples are provided to show the effect of the initial amplitude, the inclination angle, and the size of a borehole on the sinusoidal and helical buckling behaviors of CT with the residual bending.

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

Journal of Mechanisms and Robotics ◽

10.1115/1.4027699 ◽

2014 ◽

Vol 6 (4) ◽

Cited By ~ 5

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.

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On the Mechanical Behavior of the Orthotropic Cord-Rubber Composite

Tire Science and Technology ◽

10.2346/1.2167223 ◽

1976 ◽

Vol 4 (4) ◽

pp. 219-232 ◽

Cited By ~ 2

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.

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Discrete element model for general polyhedra

Computational Particle Mechanics ◽

10.1007/s40571-021-00415-z ◽

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.

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Towards Recognition of Scale Effects in a Solid Model of Lattices with Tensegrity-Inspired Microstructure

Solids ◽

10.3390/solids2010002 ◽

2021 ◽

Vol 2 (1) ◽

pp. 50-59

Author(s):

Wojciech Gilewski ◽

Anna Al Sabouni-Zawadzka

Keyword(s):

Mechanical Properties ◽

Continuum Model ◽

Scale Effects ◽

Theory Of Elasticity ◽

Solid Model ◽

Gradient Theory ◽

General Description ◽

Normal Forces ◽

Second Gradient ◽

Proposed Model

This paper is dedicated to the extended solid (continuum) model of tensegrity structures or lattices. Tensegrity is defined as a pin-joined truss structure with an infinitesimal mechanism stabilized by a set of self-equilibrated normal forces. The proposed model is inspired by the continuum model that matches the first gradient theory of elasticity. The extension leads to the second- or higher-order gradient formulation. General description is supplemented with examples in 2D and 3D spaces. A detailed form of material coefficients related to the first and second deformation gradients is presented. Substitute mechanical properties of the lattice are dependent on the cable-to-strut stiffness ratio and self-stress. Scale effect as well as coupling of the first and second gradient terms are identified. The extended solid model can be used for the evaluation of unusual mechanical properties of tensegrity lattices.

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

Volume 5A: 42nd Mechanisms and Robotics Conference ◽

10.1115/detc2018-86204 ◽

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.

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