Abstract: Since the first studies dedicated to the mechanics of deformable bodies (by Euler, D’Alembert, Lagrange) the principle of virtual work (or virtual velocities) has been used to provide firm guidance to the formulation of novel theories. Gabrio Piola dedicated his scientific life to formulating a continuum theory in order to encompass a large class of deformation phenomena and was the first author to consider continua with non-local internal interactions and, as a particular case, higher-gradient continua. More recent followers of Piola (Mindlin, Sedov and then Richard Toupin) recognized the principle of virtual work (and its particular case, the principle of least action) as the (only!) firm foundation of continuum mechanics. Mindlin and Toupin managed to formulate a conceptual frame for continuum mechanics which is able to effectively model the complex behaviour of so-called architectured, advanced, multiscale or microstructured (meta)materials. Other postulation schemes, in contrast, do not seem able to ...

Abstract: In this work, a nonlocal zeroth-order shear deformation theory is developed for the nonlinear postbuckling behavior of nanoscale beams. The beauty of this formulation is that, in addition to including the nonlocal effect according to the nonlocal elasticity theory of Eringen, the shear deformation effect is considered in the axial displacement within the use of shear forces instead of rotational displacement like in existing shear deformation theories. The principle of virtual work together of the nonlocal differential constitutive relations of Eringen, are considered to obtain the equations of equilibrium. Closed-form solutions for the critical buckling load and the amplitude of the static nonlinear response in the postbuckling state for simply supported and clamped clamped nanoscale beams are determined.

Abstract: There is evidence that much virtual work takes place beyond traditionally studied contexts, arising organically as part of ongoing work flow. As this unstructured virtual work becomes increasingly ...

Abstract: Several efforts have been made in the last years to improve the efficiency and the effectiveness of structural models for the analysis of laminated shell structures. Among the others, many recent and past works in the literature have been aimed at formulating theories of structures that maximize the accuracy of analysis meanwhile reducing the computational costs. In this paper, this objective is pursued by implementing advanced shell theories with through-the-thickness variable kinematic capabilities. By employing the Carrera Unified Formulation (CUF), the proposed shell model is obtained by expressing the displacement field as an arbitrary and, eventually, hierarchical expansion of the primary unknowns along the thickness. Thus, Equivalent-Single-Layer (ESL), Layer-Wise (LW) models as well as variable kinematic models which combine ESL and LW approaches within the shell thickness can be obtained in a straightforward and unified manner. After the unified shell model is formulated, the governing equations and the related finite element arrays are obtained by employing the principle of virtual work. A nine node finite element is implemented to approximate the solution field, and the Mixed Interpolation of Tensorial Components (MITC) method is used to contrast the membrane and shear locking phenomena. Some numerical examples are discussed, including three- and ten-layered cross-ply shells under bi-sinusoidal load and simply-supported boundary conditions, a multilayered spherical panel subjected to bi-sinusoidal load and a sandwich cylinder undergoing bi-sinusoidal pressure. Moreover, various thickness and radius-to-thickness ratios are considered. Whenever possible, the results are compared with those from the literature and from exact elasticity solutions. The analysis of the results clearly shows the enhanced capabilities of the present variable-kinematic shell element, which allows the analyst to opportunely reduce the computational costs and enhance the accuracy of the model only in those regions of the thickness domain where an accurate evaluation of the stress/strain field is needed.

Abstract: In order to meet the requirements of large downward force and high stiffness performance for the friction stir welding process, this paper proposes a 5 degree-of-freedom hybrid manipulator as friction stir welding robot. It is composed of a 3 degree-of-freedom redundant parallel module and a 2 degree-of-freedom rotating head. Semi-analytical stiffness model of the hybrid manipulator is firstly established by compliance models of the two substructures. Virtual work principle, deformation superposition principle and twist/wrench mapping model are applied to this compliance modeling process. A novel instantaneous stiffness performance index is then proposed on the basis of instantaneous energy defined by reciprocal product of external payload screw and corresponding deformation screw. It solves the problems of inconsistent physical unit of linear/angular stiffness and is able to evaluate overall and worst-case stiffness performance. Next, stiffness/compliance experiments are carried out to verify the stiffne...

Abstract: Summary Among all 3D 8-node hexahedral solid elements in current finite element library, the ‘best’ one can produce good results for bending problems using coarse regular meshes. However, once the mesh is distorted, the accuracy will drop dramatically. And how to solve this problem is still a challenge that remains outstanding. This paper develops an 8-node, 24-DOF (three conventional DOFs per node) hexahedral element based on the virtual work principle, in which two different sets of displacement fields are employed simultaneously to formulate an unsymmetric element stiffness matrix. The first set simply utilizes the formulations of the traditional 8-node trilinear isoparametric element, while the second set mainly employs the analytical trial functions in terms of 3D oblique coordinates (R, S, T). The resulting element, denoted by US-ATFH8, contains no adjustable factor and can be used for both isotropic and anisotropic cases. Numerical examples show it can strictly pass both the first-order (constant stress/strain) patch test and the second-order patch test for pure bending, remove the volume locking, and provide the invariance for coordinate rotation. Especially, it is insensitive to various severe mesh distortions. Copyright © 2016 John Wiley & Sons, Ltd.

Abstract: High specific strength and stiffness are characteristics desired for aircraft and launch vehicle domains to enhance the payload gain and performance. The mechanical properties of the composites can be further tailored by embedding structural components, such as shape memory alloys, into the passive composite structure. The present study is primarily focused on the nonlinear free vibration analysis of spherical and cylindrical composite shell panels embedded with shape memory alloy fibers. The nonlinear finite element governing equations based on the higher-order shear deformation plate theory and principle of virtual work with nonlinear von-Karman strain displacement relations are employed for the analysis. The temperature-dependent material properties of shape memory alloy are considered in the formulation. A nine-noded isoperimetric element is accounted for synthesizing the element for the finite formulation. The Young's modulus and the recovery stress vary with temperature and higher nonlineari...

Abstract: In today’s competitive business environment, virtual work settings present a growing challenge for rapid solutions of organization’s complex problems. This enables an organization to pool talent and expert employees by eradicating the time and space barriers. In accordance, companies are profoundly investigating on virtual teams’ performance enhancement. Virtual work settings revolutionize workplace by providing high level of responsiveness and flexibility. Virtual work setting has also many issues and challenges which must be addressed in order to enhance the team’s performance. Hence one of the major challenge of modern work setting is virtual leadership. This review paper presents an introduction to virtual leaderships, advantages of virtual work environment, challenges and recommendations for virtual leaders to enhance the performance of virtual teams. This article also offers review of earlier published researches and reports the findings on virtual team leadership in a struggle to the present the current state of work on this topic. DOI: 10.5901/mjss.2017.v8n4s1p183

Abstract: The paper is devoted to non-linear vibrations of plates, made of the Zener viscoelastic material modelled with the Caputo fractional derivative, and in particular to their response to harmonic excitation. The plate geometric non-linearity is of the von Karman type. In the formulation shear effects and rotary inertia are considered, too. The problem is solved in the frequency domain. A one-harmonic form of the solution for plate displacements corresponding to the plate formulation is assumed. The amplitude equation is obtained from the time averaged principle of virtual work. The time averaging precedes the use of the harmonic balance method. In the space discretization the finite element method is used involving 8-noded rectangular plate elements with selective-reduced integration. Several numerical examples are analyzed and the response curves are found using a path-following method. The purpose of these analyses is to identify material features of the adopted model of viscoelasticity with the fractional derivative.

Abstract: In the present work, a close-form solution based on a unified one-dimensional model is proposed and then applied to static response analyses of cross-ply laminated and sandwich beams subjected to simply supported boundary conditions. The hierarchical beam model is derived within the framework of the Carrera Unified Formulation (CUF), which makes use of Lagrange polynomials to express the three-dimensional (3D) displacement field via arbitrary order approximation of pure displacement variables at each layer over the cross section, in a Layer-Wise (LW) sense. The governing equations are derived via the principle of virtual work and a Navier-type close-form solution is employed to solve the resulting boundary value problem. Four benchmark numerical examples are carried out to demonstrate the efficiency of this novel method, including compact multi-layered cross-ply laminated beams, a thin-walled composite box beam and a composite sandwich-box beam. The results show that accurate displacement and stress components can be obtained as the order of the expansion increases, accompanied by a significant reduction in computational costs in comparison with the 3D finite element solutions. Besides, numerical cases in this research may be taken as benchmarks for future assessments in this field.

Abstract: Summary A class of mixed interpolated beam elements is introduced in this paper under the framework of the Carrera Unified Formulation (CUF) to eliminate the detrimental effects due to shear locking. The Mixed Interpolation of Tensorial Components (MITC) method is adopted to generate locking-free displacement-based beam models using general 1D finite elements. An assumed distribution of the transverse shear strains is employed for the derivation of the virtual work and the full Gauss-Legendre quadrature is used for the numerical computation of all the components of the stiffness matrix. Linear, quadratic and cubic beam elements are developed using the unified formulation and applied to linear static problems including compact, laminated and thin-walled structures. A comprehensive study of how shear locking affects general beam elements when different classical integration schemes are employed is presented, evidencing the outstanding capabilities of the MITC method to overcome this numerical issue. Refined beam theories based on the expansion of pure and generalized displacement variables are implemented making use of Lagrange and Legendre polynomials over the cross-sectional domain, allowing one to capture complex states of stress with a 3D-like accuracy. The numerical examples are compared to analytic, numerical solutions from the literature, and commercial software solutions, whenever it is possible. The efficiency and robustness of the proposed method is demonstrated throughout all the assessments, illustrating that MITC elements are the natural choice to avoid shear locking and showing an unprecedent accuracy in the computation of transverse shear stresses for beam formulations. This article is protected by copyright. All rights reserved.

Abstract: Modeling and analysis of complex dynamical systems can be effectively performed using multibody system (MBS) simulation software. Many modern MBS packages are able to efficiently and reliably handle rigid and flexible bodies, often offering a wide choice of different formulations. Despite many advances in modeling of flexible systems, the most widely used formulation remains the well-established floating frame of reference formulation (FFRF). Although FFRF usually allows inclusion of only small elastic deformations, this assumption is adequate for many industrial applications. In addition, FFRF is computationally efficient if implemented with appropriate model order reduction techniques and effective handling of system inertia terms by utilization of so-called inertia shape integrals. However, derivation of the system of equations of motion for FFRF bodies is a complex and often error-prone task. The main goal of this paper is to provide a reliable, detailed, universal and clear set of inertia terms within the FFRF. The paper concentrates on detailed derivation of the inertia forces with focus on accurate determination and exploitation of the inertia shape integrals. Two standard methods are employed, namely the Lagrangian and Virtual Work approaches. Additionally, the introduced derivations are executed without selection of specific rotational parameters. Direct application of Euler parameters and Euler angles is presented. It is found that the derived expressions are well suited for direct implementation and simplify derivation of force components.

Abstract: The working device is the most important component of an excavator. It directly determines the longevity, stability, and economy of an excavator. With the Denavit–Hartenberg convention and the virtual work principle, this study establishes a mathematical model to analyze and optimize the hydraulic excavator working device. A virtual prototype is built in ADAMS/View to verify the kinematic and dynamic models. The simulation result proves the accuracy of the mathematic model. A set of performance indexes, including workspace, digging force, mechanical efficiency, and transmission ability, are presented based on the dynamic analysis model. To increase the digging force and the mechanical efficiency, the modified parallel particle swarm optimization algorithm is applied to optimize the joint position and linkage length. An improvement of 5.57% in the total performance is achieved. This improvement confirms the stability and efficiency of the optimization model. The mathematical model can be used for new excavator designs.

Abstract: We devise and evaluate numerically Hybrid High-Order (HHO) methods for hyperelastic materials undergoing finite deformations. The HHO methods use as discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton, together with cell-based polynomials that can be eliminated locally by static condensation. The discrete problem is written as the minimization of the broken nonlinear elastic energy where a local reconstruction of the displacement gradient is used. Two HHO methods are considered: a stabilized method where the gradient is reconstructed as a tensor-valued polynomial of order $k$ and a stabilization is added to the discrete energy functional, and an unstabilized method which reconstructs a stable higher-order gradient and circumvents the need for stabilization. Both methods satisfy the principle of virtual work locally with equilibrated tractions. We present a numerical study of both HHO methods on test cases with known solution and on more challenging three-dimensional test cases including finite deformations with strong shear layers and cavitating voids. We assess the computational efficiency of both methods, and we compare our results to those obtained with an industrial software using conforming finite elements and to results from the literature. Both methods exhibit robust behavior in the quasi-incompressible regime.

Abstract: Flexure mechanisms provide guided motion via elastic deformation of thin beams. Due to the employment of compliant elements, these mechanisms cannot sufficiently maintain acceptable constraint stiffness level in the entire range of motion. The stiffness deterioration afflicts the performance of flexure mechanisms in terms of motion range, accuracy and constraint characteristics. This paper presents a novel flexure beam module with improved constraint behavior in beam-based flexure mechanisms. The proposed module alleviates the problem of stiffness loss in large displacements and provides a better motion performance. The mathematical model governing the static behavior of the module is developed using the principle of virtual work. The geometric nonlinearity associated with large midplane stretching is taken into account. Closed-form solutions are derived for load-displacement relationships, providing a powerful design tool for the novel flexure. Also a nonlinear expression is obtained for the strain energy of the flexure in terms of end displacements. The functionality of the presented module is exploited in a multi-beam parallelogram mechanism. The constraint behavior of the parallelogram is analytically quantified and considerable improvements in stiffnesses and error motions are observed. The analytical results provided in this paper are verified via finite element simulations. The proposed novel module can be used as the building block of more complex flexures to improve their stiffness characteristics, diminish their error motions and widen their stability region.

Abstract: A stiffness of the parallel manipulators with linear limbs is analyzed by considering the inertial wrench of the moving links and the constrained wrench. First, a formula is derived for solving the dynamic active and constrained wrenches, the inertial wrench of moving links based on the principle of virtual work. Second, the relationship between the elastic deformations of limbs and the dynamic active/constrained wrench and the inertial wrench of moving links are discovered and analyzed. Third, a unified stiffness model of parallel manipulators is established by considering the inertial wrench of moving links and the dynamic active/constrained wrench. Fourth, a unified formula is derived for solving the elastic deformations of the moving platform by considering the inertial wrench of the moving links and the dynamic active/constrained wrenches. Finally, an analytic numerical example of the 3SPR-type parallel manipulator is given for solving its stiffness and elastic deformation. The correctness of derived formulae of the stiffness and the elastic deformations are verified by the analytic numerical solutions. Derive formula of dynamic wrenches, inertial wrench of parallel manipulators.Discoverer relationship between deformations and dynamic and inertial wrench.Establish unified whole dynamic stiffness modeling of parallel manipulators.Derive unified formula for solving elastic deformations by considering inertial wrench.Give numerical example of 3SPR PM for solving dynamic stiffness, elastic deformation.

Abstract: A new piezoelectric tool actuator (PETA) for elliptical vibration turning has been developed based on a hybrid flexure hinge connection. Two double parallel four-bar linkage mechanisms and two right circular flexure hinges were chosen to guide the motion. The two input displacement directional stiffness were modeled according to the principle of virtual work modeling method and the kinematic analysis was conducted theoretically. Finite element analysis was used to carry out static and dynamic analyses. To evaluate the performance of the developed PETA, off-line experimental tests were carried out to investigate the step responses, motion strokes, resolutions, parasitic motions, and natural frequencies of the PETA along the two input directions. The relationship between input displacement and output displacement, as well as the tool tip's elliptical trajectory in different phase shifts was analyzed. By using the developed PETA mechanism, micro-dimple patterns were generated as the preliminary application to demonstrate the feasibility and efficiency of PETA for elliptical vibration turning.

Abstract: The aim of this paper is to compare the accuracy of the absolute nodal coordinate formulation and the floating frame of reference formulation for the rigid-flexible coupling dynamics of a three-dimensional Euler–Bernoulli beam by numerical and experimental validation. In the absolute nodal coordinate formulation, based on geometrically exact beam theory and considering the torsion effect, the material curvature of the beam is derived, and then variational equations of motion of a three-dimensional beam are obtained, which consist of three position coordinates, two slope coordinates, and one rotational coordinate. In the floating frame of reference formulation, the displacement of an arbitrary point on the beam is described by the rigid-body motion and a small superimposed deformation displacement. Based on linear elastic theory, the quadratic terms of the axial strain are neglected, and the curvatures are simplified to the first order. Considering both the linear damping and the quadratic air resistance damping, the equations of motion of the multibody system composed of air-bearing test bed and a cantilevered three-dimensional beam are derived based on the principle of virtual work. In order to verify the results of the computer simulation, two experiments are carried out: an experiment of hub–beam system with large deformation and a dynamic stiffening experiment. The comparison of the simulation and experiment results shows that in case of large deformation, the frequency result obtained by the floating frame of reference formulation is lower than that obtained by the experiment. On the contrary, the result obtained by the absolute nodal coordinate formulation agrees well with that obtained by the experiment. It is also shown that the floating frame of reference formulation based on linear elastic theory cannot reveal the dynamic stiffening effect. Finally, the applicability of the floating frame of reference formulation is clarified.