Virtual Work Theory Research Articles

Interlayer reinforced 3D printed concrete with recycled coarse aggregate: Shear properties and enhancement methods

In reinforced 3D printed concrete structures, the shear interaction between the rebar and the 3D printed filaments influences both the performance and safety of the concrete structures during service. In this study, the shear performance of the interlayer reinforced interface (IRI) of 3D printed concrete with recycled coarse aggregates (3DPRAC) was investigated, focusing on the pore structure characteristics of the interlayer interface. An enhancement method for the IRI was proposed by varying the number of anchored rebar nails (ARNs) and comparing the results with those of 3D printed concrete with natural coarse aggregates (3DPNAC) and 3D printed mortar (3DPM). The results showed that the ARNs significantly improved the IRI shear strength of 3DPRAC. Specifically, the IRI shear strength of 3DPRAC was 6.1% lower than that of 3DPNAC but 43.6% higher than that of 3DPM. By examining the structural characteristics of the rebar-3DPRAC bonding area, a relationship between pore defects and shear strength was established. This established relationship led to the proposal of a partition model for the interlayer bonding interface. A finite element model of 3D printed concrete incorporating real pore structure characteristics was developed to analyze the stress distribution and damage characteristics of the interface under shear stress. The fracture mode induced by local pores with the crack propagation mechanism was also analyzed. Finally, a unified formula for calculating the shear strength of the 3DPRAC IRI was derived based on the principles of virtual work and plastic limit theory. This study provides theoretical support for engineering applications of 3D-printed reinforced concrete structures.

Generalized model and performance analysis of two-axis flexure hinges based on quadratic rational Bézier curve

This article presents a generalized model of two-axis flexure hinges based on quadratic rational Bézier curve. The generalized closed-form compliance equations are derived based on the virtual work theory and the superposition relationship of the deformation. Then, how to determine the number of sensitive axes, the location of the primary and secondary sensitive axes, and the configuration of the notch profile are discussed. There are 20 types of notch profiles derived from single or mixed, symmetrical or asymmetrical curves. And, the correctness of the compliance equations is verified by finite-element analysis. The maximum relative error does not exceed 10%. Finally, the precision of rotation, the maximum stress, and the effect of structural parameters on the compliance are analyzed. The results show that for two-axis flexure hinges with a flush single curve notch profile, the proximity of the center of rotation to the load end does not significantly affect the axial compliance as well as the torsional compliance. For hybrid two-axis flexure hinges with symmetric structure, the ability to maintain the center of rotation under lateral forces is better than that under the same torque. The proposed generalized model provides a reference for the design of spatial compliant mechanisms.

Experimental and theoretical studies on the lateral collapse of mechanically lined pipes

The mechanically lined pipe, which consists of a thin non-corrosive liner and a carbon steel pipe, is an economical way to transport acidic fluid in offshore applications. However, it is prone to lateral loading and potentially develops plastic collapse and liner separation during the operational stage. The present study examines its crushing performance using small-scale 2-inch lined pipes manufactured by a customized hydroforming facility. The lined pipes comprised a seamless GB45 carbon steel tube and a grade T2 copper liner. Four ring specimens extracted from lined pipes and two single-layer rings were crushed on a universal testing machine in a quasi-static manner. The tube was found to develop an ovalized shape initially and then changed into a "∞" shape in the end. The carrier and liner were found to stay together throughout the crushing process, with slight liner separation taking place. The manufacture and lateral collapse processes were also reproduced with finite element models and nonlinear analytical formulation. The analytical model was established based on the principle of virtual work and nonlinear ring theory, assuming small strain and finite rotation. It showed that the analytical and numerical simulation results agreed with the experimental results. The influence of major parameters of the problem was also studied based on the full-scale lined pipe. Amongst other findings, manufacture-related plastic hardening is shown to affect the load-carrying capacity and the growth of separation during lateral collapse.

Numerical and theoretical analysis of staggered cruciform stubs

The stiffened top-and-seat angle (STSA) connection has seen sensitive use due to its considerable stiffness, resistance, and replaceability. However, the requirement for ductility prevents further resistance enhancement. This issue could be solved by a new improved configuration (termed staggered large STSA), but it is urgent to evaluate the mechanical property and parameter influence. This paper employs the component method to conduct a numerical and theoretical investigation of the critical tensile component-cruciform stub, taking into account the influences of stub thickness, bolt pattern, and bolt diameter. With the theory of plates and shells, a model for predicting initial stiffness is proposed to provide a detailed design procedure. In addition, the paper simplifies and verifies the method for plastic resistance based on the theory of virtual work. These methods are followed by a suitable curve model to depict the tensile behavior of staggered cruciform stubs. The average prediction error is less than 10%.

Impact Coefficient Analysis of Curved Box Girder Bridge Based on Vehicle-Bridge Coupling

In the current vehicle-bridge dynamics research studies, displacement impact coefficients are often used to replace the moment and shear force impact coefficients, and the vehicle model is also simplified as a moving-load model without considering the contribution of vehicle stiffness and damping to the system in some concerned research studies, which cannot really reflect the mechanical behavior of the structures under vehicle dynamic loads. This paper presents a vehicle-bridge coupling model for the prediction of dynamic responses and impact coefficient of the long-span curved bending beam bridge. The element stiffness matrix and mass matrix of a curved box girder bridge with 9 freedom degrees are directly deduced based on the principle of virtual work and dynamic finite element theory. The vibration equations of vehicle-bridge coupling are established by introducing vehicle mode with 7 freedom degrees. The Newmark-β method is adopted to solve vibration response of the system under vehicle dynamic loads, and the influences of flatness of bridge surface, vehicle speed, load weight, and primary beam stiffness on the impact coefficient are comprehensively discussed. The results indicate that the impact coefficient presents a nonlinear increment as the flatness of bridge surface changes from good to terrible. The vehicle-bridge coupling system resonates when the vehicle speeds reach 60 km/h and 100 km/h. The moment design value will maximally increase by 2.89%, and the shear force design value will maximally decrease by 34.9% when replacing moment and shear force impact coefficients with the displacement impact coefficient for the section internal force design. The load weight has a little influence on the impact coefficient; the displacement and moment impact coefficients are decreased with an increase in primary beam stiffness, while the shear force impact coefficient is increased with an increase in primary beam stiffness. The theoretical results presented in this paper agree well with the ANSYS results.

Numerical analysis on stability of functionally graded graphene platelets (GPLs) reinforced dielectric composite plate

The present study deals with the buckling and postbuckling performances of functionally graded graphene platelets reinforced composite (FG-GPLRC) plate under external electric field. The elastic and dielectric properties of GPLRC are evaluated by effective medium theory (EMT) while the Poisson's ratio is calculated by rule of mixture. The GPL distribution throughout the thickness of the structure is described by an average volume fraction and a slope factor describing functionally graded distribution. The equations governing the buckling behaviors of FG-GPLRC plate are derived on the basis of principle of virtual work and Mindlin-Reissner plate theory using von Kármán strains. Differential quadrature method (DQM) is then used to discretize the equations and direct iteration method is used to numerically solve the discrete differential equations. The results advise that the stability of FG-GPLRC plate is correlated to several factors, including the average volume fraction of GPLs, functionally graded distribution, slope factor and the parameters of the electric field. The stability of the FG-GPLRC plates could be artificially varied via adjusting parameters of external electric field. The current research is envisaged to offer supportive information to the design of smart GPLRC structures.

Cyclic tests of steel tee energy absorbers for precast exterior wall panels in steel building frames

This paper focuses on a new type of exterior wall system for steel building frames. The wall system consists of precast reinforced concrete wall panels that are bolted to the beams of a steel building frame and are equipped with the inter-panel steel tee energy absorbers. The precast wall panels and the steel tees are expected to remain elastic and absorb hysteretic energy under the frame inter-story drifts caused by earthquakes, respectively. To demonstrate the perceived benefits of the exterior wall system and investigate the behavior of the steel tee energy absorbers, a group of five specimens with each consisting of a steel frame, a pair of precast wall panels and a set of six steel tee energy absorbers were designed, constructed and tested. The test parameters varied among the specimens were the geometries of the steel tee energy absorbers and the technology adopted to develop them. The steel frame and the precast wall panels were re-used in all specimens. Each specimen was tested through a two-phase loading program which imposed the inter-story drift demands with progressively increasing and constant peak amplitudes, respectively. All the specimens sustained the maximum inter-story drift angle of 0.05 rad or larger and exhibited a stable energy dissipation response. The tests demonstrated the damage free response of the precast exterior wall panels as well as the replaceability of the steel tee energy absorbers. Based on an idealized curvature distribution in the webs of the steel tee energy absorbers, the classic beam theory, and the virtual work theory, this research established a simplified model for computing the strengths of the steel tee energy absorbers as well as their contribution to the lateral strength of the frame. The model was found to be able to provide acceptable predictions for the tested specimens and it is recommended for future design.

Nonlocal vibration characteristics of a functionally graded porous cylindrical nanoshell integrated with arbitrary arrays of piezoelectric elements

This article studies free vibration of a functionally graded porous cylindrical small-scale shell made from porous metal and ceramic based on power law distribution. It is bonded with an adjustable array of strip-like piezoelectric elements. The behavior of integrated structure is modified by change of quantity and location of the elements. Motion equations are achieved through first-order shear deformation theory and principle of virtual work. Stress-strain relations are developed via nonlocal theory. Two comparative studies are presented for validation of formulation. A parametric study is reported to investigate effects of input parameters.

Analytical and experimental investigation of the parameters in drilling flax/poly(lactic acid) bio-composite laminates

Understanding the influences of drilling parameters on machinability characteristics of NFRCs is of value to both academia and manufacturing industries. The present work investigates drilling-induced delamination and hole quality of fully biodegradable flax/poly(lactic acid) composites in response to cutting speed, feed rate, drill diameter, and drill material. Among various types of drilling-induced damages, exit-ply delamination is found to be the most destructive damage and cutting thrust force is identified as the main reason. The experimental results revealed that thrust force is highly dependent on drilling parameters where feed rate and drill material were found to be the most influential parameter on it. The choice of drill bit in terms of diameter and material has a considerable effect on the machinability. Drilling with HSS drills resulted in nearly 60% lower thrust force and better hole quality compared to that with carbide drills. While the size of delamination damage in the samples drilled at the lowest feed (0.02 mm/rev) sounds to be unrelated to cutting forces, the overall trend confirms that decreasing the value of thrust force leads to lowering delamination damages. Hence, an effective strategy in avoiding such undesirable defects is calculating the critical thrust force below which delamination is negligible. An analytical model is developed based on the theory of virtual work to determine the critical thrust force at delamination onset. Through validating with experimental data, the proposed model agrees better with a more accurate prediction than existing models.

Analytical Compliance Model for Right Circle Flexure Hinge Considering the Stress Concentration Effect

In this paper, an analytical compliance model for right circle flexure hinge (RCFH) is presented with the stress concentration in consideration. The stress concentration caused by changes in RCFH’s cross-section usually happens at the weakest point. It has been shown to seriously affect RCFH’s compliance calculation. Based on the virtual work theory, superposition relationship of the deformation, as well as Castigliano’s second theorem, RCFH’s analytical compliance model considering the stress concentration effect is established. The model is calculated as a series of closed-form equations which are related with geometric dimensions and employed material. Complicated definite integrals existing in these compliance equations are proved to be correctly calculated through comparisons with other literatures. Finally, in order to examine the validity of the established model, finite element analysis (FEA) is conducted. The relative errors between the theoretical values obtained by the established model and FEA results are found within 20% for a wide range of geometric dimensions.

Reduced Dynamic Modeling for Heavy-Duty Hydraulic Manipulators With Multi-Closed-Loop Mechanisms

A reduced dynamic modeling approach is introduced to systematically establish explicit closed-form dynamic equations for the main motion system of a heavy-duty hydraulic manipulator with multi-closed-loop mechanisms. The harmonious combination of the reduced system dynamic method with Lagrangian formulation, the principle of virtual work and screw theory greatly reduces the tedious calculation and largely simplifies the derivation of explicit control-orientated closed-form dynamic equations for complex multi-closed-loop mechanisms. Only three coupled subsystems, two Jacobian matrices, and two Hessian matrices are involved, thereby greatly reducing the order and the complexity of the closed-form dynamic equations. In addition to calculating the two Jacobian matrices by screw theory, the two Hessian matrices are also calculated straightforwardly by screw theory, thereby avoiding the difficulty in obtaining Hessian matrices by differentiating the Jacobian matrices and simplifying the calculation of the two Hessian matrices. No parts of dynamic equations are neglected in the derivation of the dynamic model. Thus, the accurate dynamic motion equations for the main motion system are obtained concisely. The derived closed-form dynamic equations are explicit with respect to the system inputs, which facilitate dynamics analysis and controller design. The experiments on the main motion system of the heavy-duty hydraulic forging manipulator demonstrate the efficiency of the proposed approach.

Optimization of plastic analysis of moment frames using modified dolphin echolocation algorithm

The analysis of structures and, in particular, the determination of their failure mode are the basic requirements in the field of civil engineering. Obtaining this information in high-rise structures or structures with complex irregular layouts is a difficult process, which even with the use of specialized computer software is very time-consuming. In recent years, meta-heuristic algorithms have been used extensively in engineering optimization problems. This research presents an automated approach to assess plastic loads and failure modes of two-dimensional frames, in which the plastic analysis of moment frames has been optimized using the modified dolphin echolocation optimization algorithm. This method is based on the creation of the basic collapse mechanisms, which, following their combination, should reach the minimum coefficient of plastic collapse loads using virtual work theory. The efficiency of this algorithm is verified using four sample frames, which, their exact solution including minimum load factor and the corresponding critical failure mode of the structure, exit in other research. Comparison of the results shows that the proposed method provides very good results with high precision and speed and also demonstrates the failure mechanism of the structure. Meanwhile, the modifications made in this method have greatly reduced the volume of calculations. Moreover, applying changes to the dolphin echolocation optimization algorithm led to the use of this optimization algorithm for binary problems for the first time, which ultimately resulted in a good convergence rate.

Design and modeling of a soft robotic surface with hyperelastic material

While most existing soft robots have tentacle-like morphology, this paper extends the morphology of a soft robot from a curve to a surface. The presented robotic surface is fabricated using hyperelastic silicone material, and its morphology and deformation can be actively controlled through two pneumatic soft bending actuators embedded along the edges. Quasi-steady-state models of the embedded actuators and the surface structure are established using the principle of virtual work and elastic plate theory, respectively, and then combined to relate the input pressure and external force to the deformation of the soft surface. The complete model is validated experimentally against a robotic prototype where the error is within 5% of the side length of the surface for a number of actuation levels.

The blast alleviation effects of a hybrid barrier system with triple energy absorbers

Blast walls on offshore topsides are designed to protect personnel and critical equipment. The traditional design that relies on the panel as the sole energy absorber is difficult to achieve the code compliances. While studies on dual absorber system such as foam cored sandwich panels overlook the boundary effects. This study investigates the blast alleviation effects of a hybrid barrier system with triple energy absorbers (i.e. panel, foam and springs), in which the foam and springs are placed at the supports to prevent weld rupture. Accordingly, a novel design concept is proposed by using flexible supports filled with polymethacrylimide foam and rotational springs, allowing the wall to slide/rotate a certain distance/angle to release the high stresses at supports and meanwhile dissipate blast energy through material deformations. The panel deflection, energy absorption and weld rupture of the proposed system are the focal points. An analytical model based on beam vibration theory and virtual work theory has been developed, in which the boundary conditions at each support are simplified as a translational spring and a rotational spring. Finite element method has been applied to corroborate the analytical model. In addition, the interaction effects between the three absorbers have been investigated through energy absorption breakdowns. In the end, a numerical comparison study with the traditional design has been presented to demonstrate the privilege of the proposed system in minimising weld rupture risk due to the high stresses being realeased through controlled displacements and rotations at supports.

Energy absorption of the ring stiffened tubes and the application in blast wall design

Thin-walled mental tubes under lateral crushing are desirable and reliable energy absorbers against impact or blast loads. However, the early formations of plastic hinges in the thin cylindrical wall limit the energy absorption performance. This study investigates the energy absorption performance of a simple, light and efficient energy absorber called the ring stiffened tube. Due to the increase of section modulus of tube wall and the restraining effect of the T-stiffener flange, key energy absorption parameters (peak crushing force, energy absorption and specific energy absorption) have been significantly improved against the empty tube. Its potential application in the offshore blast wall design has also been investigated. It is proposed to replace the blast wall endplates at the supports with the energy absorption devices that are made up of the ring stiffened tubes and springs. An analytical model based on beam vibration theory and virtual work theory, in which the boundary conditions at each support are simplified as a translational spring and a rotational spring, has been developed to evaluate the blast mitigation effect of the proposed design scheme. Finite element method has been applied to validate the analytical model. Comparisons of key design criterions such as panel deflection and energy absorption against the traditional design demonstrate the effectiveness of the proposed design in blast alleviation.

The establishment of coupled magneto-electro-thermo-elastic theory with the consideration of surface and non-local effects and its application in laminated nano-devices

A fully coupled linear two-dimensional (2D) magneto-electro-thermo-elastic (METE) laminated plate theory considering non-local and surface effects is established for the first time based on the principle of virtual work and Mindlin's theory. This theory is suitable in macro and micro scales, and these equations obtained are general and can be reduced to some cases at particular conditions. After theoretical and numerical validation, the performance of a nano-scaled energy harvester made of piezoelectric and piezomagnetic layers is studied by using of the 2D METE theory as a specific example. A critical thickness is obtained and numerical results show that surface effect plays key role on the size-dependent behavior, including the resonant frequency, output voltage, output power, and magneto-electric coupling coefficient. The present study may be useful to multi-field coupling analysis of size-dependent nanostructures.

Static analysis of singly and doubly curved panels on rectangular plan-form

In the present work, an analytical solution for the static analysis of laminated composites, functionally graded and sandwich singly and doubly curved panels on the rectangular plan-form, subjected to uniformly distributed transverse loading is presented. Mathematical formulation is based on the higher order shear deformation theory and principle of virtual work is applied to derive the equations of equilibrium subjected to small deformation. A solution methodology based on the fast converging finite double Chebyshev series is used to solve the linear partial differential equations along with the simply supported boundary condition. The effect of span to thickness ratio, radius of curvature to span ratio, stacking sequence, power index are investigated. The accuracy of the solution is checked by the convergence study of non-dimensional central deflection and moments. Present results are compared with those available in the literature.

Nonlinear free vibration analysis of shape memory alloy embedded laminated composite shell panel

ABSTRACTHigh 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 nonlinearity. The incremental method is used to generate the inputs for the temperature-dependent nonlinear properties of materials. The temperature change is divided by many small temperature increments. The temperature-dependent material properties are assumed constant during the small increment. The mechanics of shape memory alloy in substrate are presented and the governing equation of laminated composite with shape memory alloy is obtained and implemented in the MATLAB 7.8 program.

Magneto-electro-elastic buckling analysis of nonlocal curved nanobeams

In this work, a size-dependent curved beam model is developed to take into account the effects of nonlocal stresses on the buckling behavior of curved magneto-electro-elastic FG nanobeams for the first time. The governing differential equations are derived based on the principle of virtual work and Euler-Bernoulli beam theory. The power-law function is employed to describe the spatially graded magneto-electro-elastic properties. By extending the radius of the curved nanobeam to infinity, the results of straight nonlocal FG beams can be rendered. The effects of magnetic potential, electric voltage, opening angle, nonlocal parameter, power-law index and slenderness ratio on buckling loads of curved MEE-FG nanobeams are studied.

Strain Gradient Finite Element Analysis on the Vibration of Double-Layered Graphene Sheets

A nonlocal Kirchhoff plate model with the van der Waals (vdW) interactions taken into consideration is developed to study the vibration of double-layered graphene sheets (DLGS). The dynamic equations of multi-layered Kirchhoff plate are derived based on strain gradient elasticity. An explicit formula is derived to predict the natural frequency of the DLGS with all edges simply supported. Then a 4-node 24-degree of freedom (DOF) Kirchhoff plate element is developed to discretize the higher order partial differential equations with the small scale effect taken into consideration by the theory of virtual work. It can be directly used to predict the scale effect on the vibrational DLGS with different boundary conditions. A good agreement between finite element method (FEM) results and theoretical natural frequencies of the vibration simply supported double-layered graphene sheet (DLGS) validates the reliability of the FEM. Finally, this new FEM is used to investigate the effect of vdW coefficients, sizes, nonlocal parameters, vibration mode and boundary conditions on the vibration behaviors of DLGS.