Showing papers on "Virtual work published in 2013"

Finite Element Analysis of Composite Materials using Abaqus

Abstract: Mechanics of Orthotropic Materials Lamina Coordinate System Displacements Strain Stress Contracted Notation Equilibrium and Virtual Work Boundary Conditions Continuity Conditions Compatibility Coordinate Transformations Transformation of Constitutive Equations 3D Constitutive Equations Engineering Constants From 3D to Plane Stress Equations Apparent Laminate Properties Introduction to Finite Element Analysis Basic FEM Procedure General Finite Element Procedure Solid Modeling, Analysis, and Visualization Elasticity and Strength of Laminates Kinematic of Shells Finite Element Analysis of Laminates Failure Criteria Predefined Fields Buckling Eigenvalue Buckling Analysis Continuation Methods Free Edge Stresses Poisson's Mismatch Coefficient of Mutual Influence Computational Micromechanics Analytical Homogenization Numerical Homogenization Local-Global Analysis Laminated RVE Viscoelasticity Viscoelastic Models Boltzmann Superposition Correspondence Principle Frequency Domain Spectrum Representation Micromechanics of Viscoelastic Composites Macromechanics of Viscoelastic Composites FEA of Viscoelastic Composites Continuum Damage Mechanics One-Dimensional Damage Mechanics Multidimensional Damage and Effective Spaces Thermodynamics Formulation Kinetic Law in Three-Dimensional Space Damage and Plasticity Discrete Damage Mechanics Overview Approximations Lamina Constitutive Equation Displacement Field Degraded Laminate Stiffness and CTE Degraded Lamina Stiffness Fracture Energy Solution Algorithm Delaminations Cohesive Zone Method Virtual Crack Closure Technique Appendix A: Tensor Algebra Appendix B: Second-Order Diagonal Damage Models Appendix C: Software Used Index Problems appear at the end of each chapter.

Free vibration analysis of functionally graded shells by a higher-order shear deformation theory and radial basis functions collocation, accounting for through-the-thickness deformations

Abstract: This paper deals with free vibration problems of functionally graded shells. The analysis is performed by radial basis functions collocation, according to a higher-order shear deformation theory that accounts for through-the-thickness deformation. The equations of motion and the boundary conditions are obtained by Carrera’s Unified Formulation resting upon the principle of virtual work, and further interpolated by collocation with radial basis functions. Numerical results include spherical as well as cylindrical shell panels with all edges clamped or simply supported and demonstrate the accuracy of the present approach.

A generalized mechanical model for suture interfaces of arbitrary geometry

Abstract: Suture interfaces with a triangular wave form commonly found in nature have recently been shown to exhibit exceptional mechanical behavior, where geometric parameters such as amplitude, frequency, and hierarchy can be used to nonlinearly tailor and amplify mechanical properties In this study, using the principle of complementary virtual work, we formulate a generalized, composite mechanical model for arbitrarily-shaped interdigitating suture interfaces in order to more broadly investigate the influence of wave-form geometry on load transmission, deformation mechanisms, anisotropy, and stiffness, strength, and toughness of the suture interface for tensile and shear loading conditions The application of this suture interface model is exemplified for the case of the general trapezoidal wave-form Expressions for the in-plane stiffness, strength and fracture toughness and failure mechanisms are derived as nonlinear functions of shape factor β (which characterizes the general trapezoidal shape as triangular, trapezoidal, rectangular or anti-trapezoidal), the wavelength/amplitude ratio, the interface width/wavelength ratio, and the stiffness and strength ratios of the skeletal/interfacial phases These results provide guidelines for choosing and tailoring interface geometry to optimize the mechanical performance in resisting different loads The presented model provides insights into the relation between the mechanical function and the morphological diversity of suture interface geometries observed in natural systems

New Nonpolynomial Shear-Deformation Theories for Structural Behavior of Laminated-Composite and Sandwich Plates

Abstract: In the present study, new nonpolynomial shear-deformation theories are proposed and implemented for structural responses of laminated-composite and sandwich plates. The theories assume nonlinear distribution of transverse shear stresses, and also satisfy the traction-free boundary conditions at the top and bottom layers of the laminates. The governing differential equations are derived for a generalized shear-deformation theory by implementing the dynamic version of principle of virtual work and calculus of variations. A generalized closed-form solution methodology of the Navier type is implemented to ensure the validity and efficiency of the present theories for bending, buckling, and free-vibration responses of the laminated-composite and sandwich plates. It is observed that the proposed formulation in conjunction with the solution methodology is capable of handling all existing five-degree-of-freedom-based shear-deformation theories. The comparison of results also shows that the adequate choice of shea...

A nth-order shear deformation theory for the bending analysis on the functionally graded plates

Abstract: This paper focus on the bending analysis of functionally graded plates by a n th-order shear deformation theory and meshless global collocation method based on the thin plate spline radial basis function. Reddy's third-order theory can be considered as a special case of present n th-order theory ( n = 3). The governing equations are derived by the principle of virtual work. The displacement and stress of a simply supported functionally graded plate under sinusoidal load are calculated to verify the accuracy and efficiency of the present theory.

A Closed-Form Nonlinear Model for the Constraint Characteristics of Symmetric Spatial Beams

Abstract: The constraint-based design of flexure mechanisms requires a qualitative and quantitative understanding of the constraint characteristics of flexure elements that serve as constraints. This paper presents the constraint characterization of a uniform and symmetric cross-section, slender, spatial beam—a basic flexure element commonly used in three-dimensional flexure mechanisms. The constraint characteristics of interest, namely stiffness and error motions, are determined from the nonlinear load–displacement relations at the beam end. Appropriate assumptions are made while formulating the strain and strain energy expressions for the spatial beam to retain relevant geometric nonlinearities. Using the principle of virtual work, nonlinear beam governing equations are derived and subsequently solved for general end loads. The resulting nonlinear load–displacement relations capture the constraint characteristics of the spatial beam in a compact, closed-form, and parametric manner. This constraint model is shown to be accurate using nonlinear finite element analysis, within a load and displacement range of practical interest. The utility of this model lies in the physical and analytical insight that it offers into the constraint behavior of a spatial beam flexure, its use in design and optimization of 3D flexure mechanism geometries, and its elucidation of fundamental performance tradeoffs in flexure mechanism design.

A two degree of freedom micro-gripper with grasping and rotating functions for optical fibers assembling.

Abstract: In this paper, a two degree of freedom flexure-based micro-gripper is proposed and applied in the complicated assembling process of optical fibers. The design concept is modeled on the manipulation of human fingers. Therefore, the two tips of micro-gripper, just like human fingers, can easily grasp the optical fiber with a controllable force and precisely rotate it by the rubbing operation. In addition, some sensors installed on the micro-gripper can enhance the operating accuracy. In the developing process, pseudo-rigid-body model method and virtual work principle are employed to conduct theoretical design. Then the obtained theoretical model is validated and optimized by the finite element analysis. Fabrication of the micro-gripper adopts wire electro discharge machining technology and material of aluminum alloy (AL-7075). Experimental studies are carried out on the prototype to further validate the performance of micro-gripper. Experimental results indicate that the developed micro-gripper can well satisfy the requirements of our mission, which also means that it can be widely used in micro-manipulation field.

Application of Ritz functions in buckling analysis of embedded orthotropic circular and elliptical micro/nano-plates based on nonlocal elasticity theory

Abstract: A continuum model based on the nonlocal theory of elasticity is developed for buckling analysis of embedded orthotropic circular and elliptical micro/nano-plates under uniform in-plane compression. The nanoplate is considered to be rested on two-parameter Winkler-Pasternak elastic foundation. The principle of virtual work is used to derive the governing vibration and stability equations. The weighted residual statements of the equations of motion are performed and the well-known Galerkin method is employed to obtain the nonlocal “Quadratic Functional” for embedded micro/nano-plates. The Ritz functions are taken to form an expression for transverse displacement which satisfies the kinematic boundary conditions. In this way, the entire nanoplate is considered as a single super-continuum element. Employing the Ritz functions eliminates the need for mesh generation and thus large number of degrees of freedom arising in discretization methods such as finite element (FE). The results show obvious dependency of critical buckling loads on the non-locality of the micro/nano elliptical plate, especially, at very small dimensions.

The generalized Hamilton’s principle for a non-material volume

Abstract: Fundamental principles of mechanics were primarily conceived for constant mass systems. Since the pioneering works of Meshcherskii, efforts have been made in order to elaborate an adequate mathematical formalism for variable mass systems. This is a current research field in theoretical mechanics. In this paper, attention is focused on the derivation of the generalized Hamilton’s principle for a non-material volume. First studies on the subject go back at least four decades with the article of McIver (J Eng Math 7(3):249–261, 1973). However, it is curious to note that the extended form of Hamilton’s principle that is derived by McIver does not recover the Lagrange’s equation for a non-material volume which is demonstrated by Irschik and Holl (Acta Mech 153(3–4):231–248, 2002). This does suggest additional theoretical investigations. In the upcoming discussion, Reynolds’ transport theorem is consistently considered regarding the original form of the principle of virtual work, and so the generalized Hamilton’s principle for a non-material volume is properly derived. It is finally shown that the generalization of Hamilton’s principle that is here proposed is in harmony with the Lagrange’s equation which is demonstrated by Irschik and Holl.

Finding the Generalized Forces of a Series-Parallel Manipulator

Abstract: In this work the kinematic and dynamic analyses of a robot manipulator whose topology consists of parallel kinematic structures with linear actuators are approached by means of the theory of screws and the principle of virtual work. The input/output equations of velocity and acceleration are obtained by applying screw theory. Then the generalized forces of the manipulator are determined combining screw theory and the principle of virtual work. Finally, a case study, whose numerical results are compared with simulations generated with the aid of specialized software, is included.

Dynamics analysis of a 3-RRP spherical parallel manipulator using the natural orthogonal complement

Abstract: In the present research, application of the Natural Orthogonal Complement (NOC) for the dynamic analysis of a spherical parallel manipulator, referred to as SST, is presented. Both inverse and direct dynamics are considered. The NOC and the SST fully parallel robot are explained. To drive the NOC for the SST manipulator, constraints between joint variables are written using the transformation matrices obtained from three different branches of the robot. The Newton–Euler formulation is used to model the dynamics of each individual body, including moving platform and legs of the manipulator. D’Alembert’s principle is applied and Newton–Euler dynamical equations free from non-working generalized constraint forces are obtained. Finally two examples, one for direct and one for inverse dynamics are presented. The correctness and accuracy of the obtained solution are verified by comparing with the solution of the virtual work method as well as commercial multi-body dynamics software.

Free vibration analysis of quadrilateral nanoplates based on nonlocal continuum models using the Galerkin method: the effects of small scale

Abstract: Free vibration analysis of quadrilateral single-layered graphene sheets (SLGS) is carried out employing nonlocal continuum mechanics. The equations of motion of the nonlocal theory are derived using the principle of virtual work. The Galerkin method in conjunction with the natural coordinates of the nanoplate is used as a basis for the analysis. The non-dimensional natural frequencies of skew, rhombic, trapezoidal and rectangular nanoplates considering various geometrical parameters and mode numbers are obtained and for each case the effects of the small length scale are investigated.

On a virtual work consistent three-dimensional Reissner–Simo beam formulation using the quaternion algebra

Abstract: In the paper, we present the Reissner–Simo beam theory in which the rotations are represented by quaternions. From the generalized virtual work principle, where the unity constraint of the rotational quaternion is properly considered and the consistent energy complements of the rotational quaternions are employed, we derive the weak kinematic equations in the quaternion-based description. These equations are then employed in the extended virtual work principle to obtain the consistent governing equations of the three-dimensional beam in terms of the quaternion algebra. The quaternion moment equilibrium equation is analyzed, discussed, and interpreted. In numerical implementation, the standard Galerkin discretization is used to obtain the quaternion-based finite-element formulation. Various examples prove the suitability of the formulation.

Numerical Algorithm of Solving the Problem of Large Elastic-Plastic Deformation by FEM

Abstract: A numerical algorithm of the investigation of stress-strain state of the solids with large elastic-plastic deformations is described. The constitutive equations are obtained using the free energy function and yield function. The general radial return method is applied. Calculation algorithm is based on the linearized equation of virtual work, defined to actual state. The continuation method is used. The von Mises yield criterion with isotropic hardening is considered. A spatial discretization is based on the finite element method. The developed algorithm of investigation of large elastic-plastic deformations is tested on the solution of the necking of circular bar problem and a conical shell subjecting to a constant ring load. The results of solutions and comparison with results obtained by other authors are presented.

Dynamic modelling of a 3-CPU parallel robot via screw theory

Abstract: . The article describes the dynamic modelling of I.Ca.Ro., a novel Cartesian parallel robot recently designed and prototyped by the robotics research group of the Polytechnic University of Marche. By means of screw theory and virtual work principle, a computationally efficient model has been built, with the final aim of realising advanced model based controllers. Then a dynamic analysis has been performed in order to point out possible model simplifications that could lead to a more efficient run time implementation.

Engineering Mechanics Statics

Abstract: 1. Introduction. Engineering and Mechanics. Learning Mechanics. Fundamental Concepts. Units. Newtonian Gravitation. 2. Vectors. Vector Operations and Definitions. Scalars and Vectors. Rules for Manipulating Vectors. Cartesian Components. Components in Two Dimensions. Components in Three Dimensions. Products of Vectors. Dot Products. Cross Products. Mixed Triple Products. 3. Forces. Types of Forces. Equilibrium and Free-Body Diagrams. Two-Dimensional Force Systems. Three-Dimensional Force Systems. 4. Systems of Forces and Moments. Two-Dimensional Description of the Moment. The Moment Vector. Moment of a Force About a Line. Couples. Equivalent Systems. Representing Systems by Equivalent Systems. 5. Objects in Equilibrium. The Equilibrium Equations. Two-Dimensional Applications. Statically Indeterminate Objects. Three-Dimensional Applications. Two-Force and Three-Force. 6. Structures in Equilibrium. Trusses. The Method of Joints. The Method of Sections. Space Trusses. Frames and Machines. 7. Centroids and Centers of Mass 316. Centroids. Centroids of Areas. Centroids of Composite Areas. Distributed Loads. Centroids of Volumes and Lines. The Pappus-Guldinus Theorems. Centers of Mass. Definition of the Center of Mass. Centers of Mass of Objects. Centers of Mass of Composite Objects. 8. Moments of Inertia. Areas. Definitions. Parallel-Axis Theorems. Rotated and Principal Axes. Masses. Simple Objects. Parallel-Axis Theorem. 9. Friction. Theory of Dry Friction. Applications. 10. Internal Forces and Moments. Beams. Axial Force, Shear Force, and Bending Moment. Shear Force and Bending Moment Diagrams. Relations Between Distributed Load, Shear Force, and Bending Moment. Cables. Loads Distributed Uniformly Along Straight Lines. Loads Distributed Uniformly Along Cables. Discrete Loads. Liquids and Gasses. Pressure and the Center of Pressure. Pressure in a Stationary Liquid. 11. Virtual Work and Potential Energy. Virtual Work. Potential Energy. Appendix A. Review of Mathematics. Algebra. Trigonometry. Derivatives. Integrals. Taylor Series. Vector Analysis. Appendix B. Properties of Areas and Lines. Areas. Lines. Properties of Volumes and Homogeneous Objects. Answers to Even-Numbered Problems. Index.

Knowledge Sharing in Virtual Teams: The Impact on Trust, Collaboration, and Team Effectiveness.

Abstract: The practice of virtual teams has provided organizations with a convenient solution for gathering experts to collaborate online in order to accomplish organizational tasks. However, the dynamics and characteristics of virtual teams create challenges to effective collaboration. Collaboration is an important element in teamwork, team members need to collaborate to achieve the goal for which the team is established. Literature on virtual teams has been growing for over a decade with research investigated different aspects of virtual work. Trust among virtual team members has been investigated by information systems researchers as a crucial challenge for virtual teams. Knowledge sharing and management in virtual teams have been the focus of many research recently as they represent a challenge for virtual work environment; because the knowledge is scattered among geographically distributed team members with limited face to face interaction. Yet, trust and knowledge sharing are not the final outcome of teamwork, there is a gap in the literature on how trust and knowledge sharing affect collaboration and ultimately team effectiveness in virtual settings. This study extends the literature on virtual teams through investigating the relationship between knowledge sharing, trust, and collaboration among team members in virtual team settings; and how these constructs ultimately affect virtual team effectiveness. We argue that the characteristics and structure of virtual teams requires a distinctive understanding on how

Simplified PRBMs of spatial compliant multi-beam modules for planar motion

Abstract: . PRBMs (pseudo-rigid-body models) have been becoming important engineering technologies/methods in the field of compliant mechanisms to simplify the design and analysis through the use of the knowledge body of rigid-body mechanisms coupling with springs. This article addresses the PRBMs of spatial multi-beam modules for planar motion, which are composed of three or more symmetrical wire/slender beams parallel to each other where the planar twisting DOF (degree of freedom) is assumed to be very small for specific applications/loading conditions. Simplified PRBMs are firstly proposed through replacing each beam in spatial multi-beam module with a rigid-body link plus two identical spherical joints at its two ends. The characteristics factor, bending stiffness and twisting stiffness for the spherical joint are determined. Load-displacement equations are then derived for a class of spatial multi-beam modules and general spatial multi-beam modules using the virtual work principle and kinematic relationships. Finally, nonlinear FEA (finite element analysis) is employed with comparisons with the PRBMs. The present PRBMs have shown the ability to predict the primary nonlinear constraint characteristics such as load-stiffening effect, cross-axis coupling in the two primary translational directions and buckling load.

Dockable Tool Framework for Interaction with Large Scale Wall Displays

Abstract: In accordance with an aspect of the present invention, a device and a method allows for body-based interaction with 3D applications on wall displays. The interface consists of virtual dockable tools which can be unholstered, used to manipulate geometry, and holstered on the user's body. The system also utilizes proprioceptive cues to allow the user to manipulate and holster tools without visual feedback. A 3D depth camera maps 3D user position to 3D coordinates in the virtual scene. Partitioning the physical work space into a region for interaction with geometry, and a region for tool management allows for intuitive mapping between the physical and virtual work space. The system can support multiple users, including simultaneous interaction with the environment, and tool exchange between users.