Abstract: Companies increasingly rely on virtual teams. Despite numerous studies examining the challenges of geographically dispersed work, the findings are often mixed. The purpose of this article is to ide...

Abstract: Functionally graded (FG) beams are widely used in many fields. However, the corresponding beam theory is not well established. This paper begins with distinguishing the centroid and the neutral point of cross section. First, the deformation mode is mathematically suggested for axial displacement as a general higher-order form, and then orthogonally decomposed with the help of shear stress free conditions and definitions of generalized displacements (i.e. deflection, rotation and stretch). On this basis, the generalized stresses are defined together with the work conjugated generalized strains, and the decoupled constitutive relations are then derived. Next, the principle of virtual work is proposed for beam problems, and the variationally consistent higher-order theory is established for FG beams, which is as simple as that for a homogeneous beam. Finally, the present theory is demonstrated by typical FG beam problems for both the simply supported case and the clamped case. It is indicated that the analytical solution to the present modified higher-order theory can be regarded as the benchmark of FG beam problems. Furthermore, the relation with the traditional higher-order theory is clarified, which is beneficial to conduct a comparative study on different higher-order beam theories.

Abstract: We devise and evaluate numerically Hybrid High-Order (HHO) methods for hyperelastic materials undergoing finite deformations. The HHO methods use as discrete unknowns piece-wise polynomials of order k ≥ 1 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: A continuum-based model is presented for the mechanics of bidirectional composites subjected to finite plane deformations. This is framed in the development of a constitutive relation within which the constraint of material incompressibility is augmented. The elastic resistance of the fibers is accounted for directly via the computation of variational derivatives along the lengths of bidirectional fibers. The equilibrium equation and necessary boundary conditions are derived by virtue of the principles of virtual work statement. A rigorous derivation of the corresponding linear theory is developed and used to obtain a complete analytical solution for small deformations superposed on large. The proposed model can serve as an alternative 2D Cosserat theory of nonlinear elasticity.

Abstract: In the present paper, a new fifth-order shear and normal deformation theory (FOSNDT) is developed for the bi-directional bending analysis of laminated composite and sandwich plates subjected to transverse loads. This theory considered the effects of both transverse shear and normal deformations. In-plane displacements use a polynomial shape function expanded up to fifth-order in terms of the thickness coordinate to properly account the effect of transverse shear deformation. Transverse displacement is the function of x, y and z- coordinates to account the effect of transverse normal deformations i.e. thickness stretching. Hence, the present theory involves nine unknowns in the displacement field. The present theory does not require a problem dependent shear correction factor as it satisfies traction free boundary conditions at top and bottom surfaces of the plate. The governing differential equations and associated boundary conditions are obtained using the principle of virtual work. The plate is analysed for simply supported boundary conditions using Navier’s solution technique. To prove the efficiency of the present theory, the non-dimensional displacements and stresses obtained for laminated composite and sandwich plates are compared with existing exact elasticity solutions and other theories. It is observed from the comparision that the displacements and stresses obtained by the present theory are in excellent agreement with the results obtained by exact elasticity solutions compared to other higher-order plate theories available in the literature.

Abstract: This paper presents the application of the Virtual Fields Method (VFM) for the characterization of viscoelastic behaviour of rubbers. The relaxation behaviour of the rubbers following a dynamic loading event is characterized using the dynamic VFM in which full-field (two dimensional) strain and acceleration data, obtained from high-speed imaging, are analysed by the principle of virtual work without traction force data, instead using the acceleration fields in the specimen to provide stress information. Two (silicone and nitrile) rubbers were tested in tension using a drop-weight apparatus. It is assumed that the dynamic behaviour is described by the combination of hyperelastic and Prony series models. A VFM based procedure is designed and used to produce the identification of the modulus term of a hyperelastic model and the Prony series parameters within a time scale determined by two experimental factors: imaging speed and loading duration. Then, the time range of the data is extended using experiments at different temperatures combined with the time-temperature superposition principle. Prior to these experimental analyses, finite element simulations were performed to validate the application of the proposed VFM analysis. Therefore, for the first time, it has been possible to identify relaxation behaviour of a material following dynamic loading, using a technique that can be applied to both small and large deformations.

Abstract: An identification scheme that exploits the vibration response and generated voltage of an energy harvester is proposed to estimate parameters representing nonlinear piezoelectric coefficients. We develop the governing equations of a cantilever beam with tip mass and a piezoelectric layer using the generalized Hamilton's principle and by accounting for mechanical energy, virtual work, and electric enthalpy. We then use the method of multiple scales to determine the approximate solution of the response to a direct resonant excitation. We show that the nonlinear behavior captured by the method of multiple scales as approximate solution and amplitude and phase modulation equations can be used to estimate parameters of the nonlinear piezoelectric constitutive relations.An identification scheme that exploits the vibration response and generated voltage of an energy harvester is proposed to estimate parameters representing nonlinear piezoelectric coefficients. We develop the governing equations of a cantilever beam with tip mass and a piezoelectric layer using the generalized Hamilton's principle and by accounting for mechanical energy, virtual work, and electric enthalpy. We then use the method of multiple scales to determine the approximate solution of the response to a direct resonant excitation. We show that the nonlinear behavior captured by the method of multiple scales as approximate solution and amplitude and phase modulation equations can be used to estimate parameters of the nonlinear piezoelectric constitutive relations.

Abstract: This paper presents the development of Isogeometric Analysis for plate bending problems based on unified and integrated (UI) approach, which is a modification of Reissner-Mindlin plate theory for solving thick to thin plate problems. In Reissner-Mindlin, the total displacement and two rotations are independent of each other, while in this UI approach the total displacement is split into bending displacement and shear displacement which causes the rotations, curvatures and shear deformations can be defined as first, second and third derivatives of bending displacement, respectively. The virtual work of Galerkin Method is used to define bending stiffness and shear stiffness of the element. Several convergence tests were conducted to observe the performance of unified and integrated approach in rectangular plate of different types of boundaries conditions. The result of thick and thin plate showed good results despite of low number of element with fourth degree of polynomial or increasing degree of polynomial with only one element.

Abstract: This paper deals with the kinematic analysis, dynamic modeling and base inertial parameter determination of a member of multipteron parallel manipulator family, namely, Quadripteron. First, as a prerequisite for dynamic analysis, kinematic relations are obtained. By using a new geometric approach, the solution of the inverse kinematic problem is made equivalent to solve the problem of determining the intersection of two circles within a plane. Compared to other proposed methods, this approach yields more compact and closed-form solutions. The instantaneous kinematic problem is solved via employing the screw theory. Based on foregoing kinematic relations and the concept of link Jacobian matrices, the dynamic model is formulated by means of the principle of virtual work. Furthermore, in order to obtain a more compact formulation for the dynamic analysis, a reduced dynamic model is obtained by determining the base inertial parameters of the under study manipulators.

Abstract: In the present study, a new fifth-order shear and normal deformation theory (FOSNDT) is developed for the analysis of laminated composite and sandwich plates under cylindrical bending. The theory considered the effects of transverse shear and normal deformations. To account for the effect of transverse shear deformation, in-plane displacement uses polynomial shape function expanded up to fifth-order in-terms of the thickness coordinate. Transverse displacement uses derivative of shape function to account for the effect of transverse normal deformations. Therefore, the present theory involves six independent unknown variables. The theory satisfies traction free boundary conditions at top and bottom surfaces of the plate and does not require the shear correction factor. The principle of virtual work is used to obtain the variationally consistent governing differential equations and associated boundary conditions. Analytical solutions for simply supported boundary conditions are obtained using Navier’s solution technique. Non-dimensional displacements and stresses obtained using the present theory are compared with existing exact elasticity solutions and lower and higher-order theories to prove the efficacy of the present theory. The comparison shows that the displacements and stresses predicted by the present theory are in good agreement with those obtained by using the exact solution.

Abstract: In order to improve the motion accuracy of a novel soft robotic arm with extensive degree of freedom, the kinematic model is established. Firstly, a soft robotic arm composed of two single modules is designed. Each single module contains two extension pneumatic silicone actuators (EPSAs). Secondly, the kinematic model of the EPSA is established based on the superelastic material model, the geometric relationship and the virtual work principle. Then, the kinematic model of the single module is established based on the kinematic model of the EPSA and the constant curvature assumption. Next, the kinematic model of the soft robotic arm is established by using the Frenet frame. Finally, the numerical simulation is carried out based on the Obtained kinematic model. In order to verify and modify the above kinematic model, the numerical experiment is carried out based on the finite element method. The results of the two numerical experiments show that the modified kinematic model is almost identical to the finite element model, which indicates the feasibility of this modeling method and the accuracy of the established kinematic model. This study provides the necessary kinematic foundation for the control of a soft robotic arm.

Abstract: In this paper, two-dimensional thermoelastic analysis of a functionally graded nanoshell is presented based on nonlocal elasticity theory. To formulate this problem, first-order shear deformation theory (FSDT) is used for axial and radial deformations simultaneously. Material properties are assumed to be mixture of ceramic and metal based on a power law distribution. Principle of virtual work is used for derivation of the governing equations. The analytical approach is presented based on eigenvalue and eigenvector method to derive four unknown functions including radial and axial displacements and rotations along the longitudinal direction. In addition, the influence of nonlocal and in-homogeneous index parameter is studied on the responses of the system. Two-dimensional results are presented along the radial and longitudinal directions.

Abstract: In this paper, the Kant higher-order beam theory is applied to model each segment of the partial-interaction composite beams, aiming to capture as possible fidelity as the plane stress model. On this basis, the weak-form equation is obtained through the principle of virtual work. Besides, the weak-form quadrature element (WQE), as a counterpart of the conventional finite element (CFE), is derived and implemented to more efficiently solve problems, including free vibration eigenvalue analysis and dynamic responses prediction to moving loads. After the verification of all the programs developed, a series of numerical examples are given to investigate the WQE’s superiority on convergence rate and numerical smoothness over the CFE. At the end of the paper, the influences of structural damping and loads’ moving speed on impact factor of two-span continuous beams are analyzed. Numerical results show that the proposed WQE, due to the variable-order interpolation of the element, possesses overwhelmingly higher computational efficiency than the CFE, and the numerical smoothness problem in the internal force analysis is significantly alleviated by WQE method.