Showing papers on "Virtual work published in 2020"

A generalized 4-unknown refined theory for bending and free vibration analysis of laminated composite and sandwich plates and shells

Abstract: This research is devoted to investigate the bending and free vibration behaviour of laminated composite/sandwich plates and shells, by applying an analytical model based on a generalized and simple refined higher-order shear deformation theory (RHSDT) with four independent unknown variables. The kinematics of the proposed theoretical model is defined by an undetermined integral component and uses the hyperbolic shape function to include the effects of the transverse shear stresses through the plate/shell thickness; hence a shear correction factor is not required. The governing differential equations and associated boundary conditions are derived by employing the principle of virtual work and solved via Navier-type analytical procedure. To verify the validity and applicability of the present refined theory, some numerical results related to displacements, stresses and fundamental frequencies of simply supported laminated composite/sandwich plates and shells are presented and compared with those obtained by other shear deformation models considered in this paper. From the analysis, it can be concluded that the kinematics based on the undetermined integral component is very efficient, and its use leads to reach higher accuracy than conventional models in the study of laminated plates and shells.

Thermal flexural analysis of anti-symmetric cross-ply laminated plates using a four variable refined theory

Abstract: This article deals with the flexural analysis of anti-symmetric cross-ply laminated plates under nonlinear thermal loading using a refined plate theory with four variables. In this theory, the undetermined integral terms are used and the number of variables is reduced to four, instead of five or more in other higher-order theories. The boundary conditions on the top and the bottom surfaces of the plate are satisfied; hence the use of the transverse shear correction factors is avoided. The principle of virtual work is used to obtain governing equations and boundary conditions. Navier solution for simply supported plates is used to derive analytical solutions. For the validation of the present theory, numerical results for displacements and stresses are compared with those of classical, first-order, higher-order and trigonometric shear theories reported in the literature.

Managing Virtual Workers—Strategies for Success

Abstract: The dramatic increase in virtual work during the COVID-19 pandemic boosted organizational capacity for virtual work, and is likely to result in a long-term increase in the number of employees working remotely. Although virtual work has obvious advantages for both employees and organizations, it comes with many challenges. In this article, we identify the challenges inherent in virtual work today and describe their negative impact on employee stress, well-being, and performance. We argue that managers must be proactive in addressing these challenges in order to fully leverage the benefits of virtual work. We offer concrete strategies that they can use to counter the problems commonly encountered by virtual workers.

Structural Displacement Requirement in a Topology Optimization Algorithm Based on Isogeometric Entities

Abstract: This work deals with the formulation of a general design requirement on the displacement of a continuum medium in the framework of a special density-based algorithm for topology optimization. The algorithm makes use of non-uniform rational basis spline hyper-surfaces to represent the pseudo-density field describing the part topology and of the well-known solid isotropic material with penalization approach. The proposed formulation efficiently exploits the properties of the isogeometric basis functions, which allow defining an implicit filter. In particular, the structural displacement requirement is formulated in the most general sense, by considering displacements on loaded and non-loaded regions. The gradient of the structural displacement is evaluated in closed form by using the principle of virtual work. Moreover, a sensitivity analysis of the optimized topology to the integer parameters, involved in the definition of the hyper-surface, is carried out. The effectiveness of the proposed approach is proven through meaningful 2D and 3D benchmarks.

Variational approximate for high order bending analysis of laminated composite plates

Abstract: This study presents a 4 node, 11 DOF/node plate element based on higher order shear deformation theory for lamina composite plates. The theory accounts for parabolic distribution of the transverse shear strain through the thickness of the plate. Differential field equations of composite plates are obtained from energy methods using virtual work principle. Differential field equations of composite plates are obtained from energy methods using virtual work principle. These equations were transformed into the operator form and then transformed into functions with geometric and dynamic boundary conditions with the help of the Gâteaux differential method, after determining that they provide the potential condition. Boundary conditions were determined by performing variational operations. By using the mixed finite element method, plate element named HOPLT44 was developed. After coding in FORTRAN computer program, finite element matrices were transformed into system matrices and various analyzes were performed. The current results are verified with those results obtained in the previous work and the new results are presented in tables and graphs.

Dynamic buckling of classical/non-classical curved beams by nonlocal nonlinear finite element accounting for size dependent effect and using higher-order shear flexible model

Abstract: This paper investigates the dynamic snap-through buckling of classical and non-classical curved beams subjected to a suddenly applied step load The small scale effect prevalent in non-classical beams, viz, micro and nanobeam, is modeled using the nonlocal elasticity approach The formulation accounts for moderately large deflection and rotation The governing equilibrium equations are derived using the dynamic version of the principle of virtual work and are subsequently simplified in terms of the generalized displacements for the development of a nonlocal nonlinear finite element model The spatial domain comprises of 3-noded higher-order curved beam elements based on shear flexible theory associated with sine function The nonlinear governing equations are solved using the incremental stiffness matrices and by adopting direct time integration method The critical dynamic buckling load is identified by the smallest load at which there is a sudden rise in the amplitude of vibration The efficacy of model here is compared against the available analytical studies for the local and nonlocal beams A detailed study is made to highlight the effects of the geometric parameter, initial condition, nonlocal parameter, load duration, and boundary conditions on the dynamic stability of both classical and non-classical curved beams The nature and degree of participation of various eigen modes accountable for the dynamic snap-through behavior are examined a posteriori using the modal expansion approach Some interesting observations made here are valuable for the optimal design of such structural members against fatigue and instability

A refined dynamic finite-strain shell theory for incompressible hyperelastic materials: equations and two-dimensional shell virtual work principle

Abstract: Based on previous work for the static problem, in this paper, we first derive one form of dynamic finite-strain shell equations for incompressible hyperelastic materials that involve three shell constitutive relations. In order to single out the bending effect as well as to reduce the number of shell constitutive relations, a further refinement is performed, which leads to a refined dynamic finite-strain shell theory with only two shell constitutive relations (deducible from the given three-dimensional (3D) strain energy function) and some new insights are also deduced. By using the weak formulation of the shell equations and the variation of the 3D Lagrange functional, boundary conditions and the two-dimensional shell virtual work principle are derived. As a benchmark problem, we consider the extension and inflation of an arterial segment. The good agreement between the asymptotic solution based on the shell equations and that from the 3D exact one gives verification of the former. The refined shell theory is also applied to study the plane-strain vibrations of a pressurized artery, and the effects of the axial pre-stretch, pressure and fibre angle on the vibration frequencies are investigated in detail.

Bending Analysis of Functionally Graded Nanoscale Plates by Using Nonlocal Mixed Variational Formula

Abstract: This work is devoted to the bending analysis of functionally graded (FG) nano-scale plate by using the nonlocal mixed variational formula under simply supported edge conditions. According to Eringen’s nonlocal elasticity theory, the mixed formula is utilized in order to obtain the governing equations. The system of equations is derived by using the principle of virtual work. The governing equations include both the small and the mechanical effects. The impact of the small-scale parameter, aspect and thickness nano-scale plate ratios, and gradient index on the displacement and stresses are explored, numerically presented, and discussed in detail. Different comparisons are made to check the precision and validity of the bending outcomes obtained from the present analysis of FG nano-scale plates. Parametric examinations are then performed to inspect the impacts of the thickness of the plate on the by and large mechanical reaction of the practically evaluated plates. The displayed outcomes are valuable for the configuration procedures of keen structures and examination from materials.

On a micropolar theory of growing solids

Abstract: The present paper is devoted to the problem of boundary conditions formulation in the growing micropolar solid mechanics. The static equations of the micropolar continuum in terms of relative tensors (pseudotensors) are derived due to virtual work principle for a solid of constant staff. The constitutive quadratic form of the elastic potential (treated as an absolute scalar) for a linear hemitropic micropolar solid is presented and discussed. The constitutive equations for symmetric and antisymmetric parts of force and couple stress tensors are given. The final forms of the static equations for the hemitropic micropolar continuum in terms of displacements and microrotations rates are obtained including the case of growing processes. A transformation of the equilibrium equations is proposed to obtain boundary conditions on the propagating growing surface in terms of relative tensors in the form of differential constraints. Those are valid for a wide range of materials and metamaterials. The algebra of rational relative invariants is intensively used for deriving the constitutive relations on the growing surface. Systems of joint algebraic rational relative invariants for force, couple stress tensors and also unit normal and tangent vectors to propagating growing surface are obtained, including systems of invariants sensitive to mirror reflections and 3D-space inversions.

Enriched continuum for multi-scale transient diffusion coupled to mechanics

Abstract: In this article, we present a computationally efficient homogenization technique for linear coupled diffusion–mechanics problems. It considers a linear chemo-mechanical material model at the fine scale, and relies on a full separation of scales between the time scales governing diffusion and mechanical phenomena, and a relaxed separation of scales for diffusion between the matrix and the inclusion. When the characteristic time scales associated with mass diffusion are large compared to those linked to the deformation, the mechanical problem can be considered to be quasi-static, and a full separation of scales can be assumed, whereas the diffusion problem remains transient. Using equivalence of the sum of virtual powers of internal and transient forces between the microscale and the macroscale, a homogenization framework is derived for the mass diffusion, while for the mechanical case, considering its quasi-static nature, the classical equivalence of the virtual work of internal forces is used instead. Model reduction is then applied at the microscale. Assuming a relaxed separation of scales for diffusion phenomena, the microscopic fields are split into steady-state and transient parts, for which distinct reduced bases are extracted, using static condensation for the steady-state part and the solution of an eigenvalue problem for the transient part. The model reduction at the microscale results in emergent macroscopic enriched field variables, evolution of which is described with a set of ordinary differential equations which are inexpensive to solve. The net result is a coupled diffusion–mechanics enriched continuum at the macroscale. Numerical examples are conducted for the cathode–electrolyte system characteristic of a lithium ion battery. The proposed reduced order homogenization method is shown to be able to capture the coupled behavior of this system, whereby high computational gains are obtained relative to a full computational homogenization method.

Improved method for shear lag analysis of thin-walled box girders considering axial equilibrium and shear deformation

Abstract: The conventional method (CM) for shear lag analysis of thin-walled box girders supposes that the neutral axis coincides with the centroidal axis of the whole cross section, and thus neglects the axial equilibrium condition. An analytical method considering axial equilibrium and shear deformation, which is referred to as PM, is proposed for overcoming the defect of the conventional method. The longitudinal displacement of the web is introduced to satisfy the axial equilibrium condition and locate the neutral axis automatically. The shear deformation is considered according to the Timoshenko beam theory. Three independent shear lag functions are adopted for describing different shear lag intensities of the top, bottom and cantilever slabs. The governing differential equations for the displacement variables are deduced by means of the virtual work theorem and solved with the relevant boundary conditions. The analytical solution is then derived for the distance from the neutral axis to the top fiber of the cross section. The accuracy of the proposed method is validated by comparisons with the available experimental data as well as the finite element analysis results. Moreover, the distances from the neutral axis to the top fiber, axial forces, and stress difference ratios are analyzed for typical thin-walled box girders to quantify the influence of the axial equilibrium condition. Finally, an extensive parametric study is conducted to examine the effects of various geometric parameters on the stress difference ratio under different load types. The results show that the proposed method can provide good predictions for both deflections and axial stresses, and neglecting axial equilibrium leads to considerable underestimations of axial stresses especially at the top flange-web junctions over the interior support of the continuous box girder.

Virtual work in Portugal: a literature review

Abstract: Resumo: Apesar de ter sido um dos primeiros países da Europa a introduzir disposições no direito do trabalho para promover o trabalho virtual e ter feito fortes investimentos em infraestrutura de TIC, a adoção do trabalho virtual em Portugal fica significativamente atrás da maioria dos países europeus. Este artigo examina a literatura, documentos oficiais e bancos de dados para entender esse atraso. Constatamos que, apesar da dificuldade de medir o trabalho virtual, é possível afirmar que existiam 1,8% dos trabalhadores em 2005 envolvidos em teletrabalho. Em 2010, menos de 3% estavam envolvidos neste tipo de trabalho, enquanto em 2015 subiu para 8,2%. O artigo identifica dois fatores principais que dificultam o crescimento do trabalho virtual: a estrutura legal e os aspetos organizacionais do trabalho.

Study on the Magnetic Forces of the Dipole in the SPERF

Abstract: The Space Plasma Environment Research Facility (SPERF) in Harbin, China, is a user facility dedicated to studying space plasma physics on ground. Magnetic forces are critical to the reliable operation of a magnetic system. A dipole magnet plays a central role in the system and its force conditions are extremely complicated. So, the magnetic force of the dipole magnet is studied in this article. The magnetic system is first introduced. Then, the virtual work principle is presented to evaluate the force analytically. Not dedicated to the complex analytical computation, the qualitative analysis is done based on the breaking of the symmetry of the system from the perspective of the dipole. To validate the qualitative results and solve the force precisely, the finite-element analysis in ANSYS Maxwell is performed. The force results are analyzed and regular patterns are obtained. The influence of the spatial position and the eddy current are studied. In a complex system, the dipole forces from different source magnets compete to dominate as the time proceeds. The methods for analyzing the magnetic forces can easily be extended to other electromagnetic systems.

An extended Hamilton principle as unifying theory for coupled problems and dissipative microstructure evolution.

Abstract: An established strategy for material modeling is provided by energy-based principles such that evolution equations in terms of ordinary differential equations can be derived. However, there exist a variety of material models that also need to take into account non-local effects to capture microstructure evolution. In this case, the evolution of microstructure is described by a partial differential equation. In this contribution, we present how Hamilton's principle provides a physically sound strategy for the derivation of transient field equations for all state variables. Therefore, we begin with a demonstration how Hamilton's principle generalizes the principle of stationary action for rigid bodies. Furthermore, we show that the basic idea behind Hamilton's principle is not restricted to isothermal mechanical processes. In contrast, we propose an extended Hamilton principle which is applicable to coupled problems and dissipative microstructure evolution. As example, we demonstrate how the field equations for all state variables for thermo-mechanically coupled problems, i.e. displacements, temperature, and internal variables, result from the stationarity of the extended Hamilton functional. The relation to other principles, as principle of virtual work and Onsager's principle, are given. Finally, exemplary material models demonstrate how to use the extended Hamilton principle for thermo-mechanically coupled rate-dependent, rate-independent, and gradient-enhanced materials.

A study on vibrations of hexarot-based high-G centrifugal simulators

Abstract: This paper investigates the vibrations of hexarot simulators. The generalized modeling of kinematics and dynamics formulation of a hexarot mechanism is addressed. This model considers the flexible manipulator with the base motion. The dynamic formulation has been developed based on the principle of virtual work. The dynamic model consists of the stiffness of the different parts of the mechanism, the effects of gravity and inertia, torque and force related to the joints viscous friction. Finally, the response of the end effector at various frequencies has been presented, and the vibrations of the mechanism and the dynamic stability index have been investigated.