Uniform Mechanical Loading Research Articles

Nonlinear bending and buckling analysis of 3D-printed meta-sandwich curved beam with auxetic honeycomb core

The present study investigates the static responses of a 3D-printed polymeric meta-sandwich curved beam with an auxetic honeycomb core, including buckling and nonlinear bending behavior. After extracting the mechanical properties of the core material, the nonlinear governing equations for the curved beam under two types of loading, namely uniform transverse and axial mechanical loads, are derived based on the first-order shear deformation theory and von-Kármán nonlinearity. After examining the convergence of the static responses and validating them by using the Ritz method, the influence of various geometrical parameters of the 3D-printed meta-sandwich structure on the results of buckling and nonlinear bending behavior as well as their optimization using the response surface methodology (RSM) are studied. The results indicate that by increasing the thickness-to-length ratio of the inclined wall, the critical load of the auxetic sandwich beam is enhanced due to improved stiffness, and its lateral displacement declines. The amount of buckling load increase from m = 0.005 to m = 0.1 is 1.92% in the clamped-clamped boundary conditions, 1.56% in the clamped-simply supported conditions, and 1.2% in the simply supported-simply supported edge conditions. Therefore, by selecting appropriate geometrical parameters for the core cells, the occurrence of instability can be delayed, leading to enhanced buckling resistance of the structure. Furthermore, optimizing the results by using the RSM showed that the highest critical load value and the lowest transverse deflection value of the meta-sandwich curved beam are obtained when θc = 15, n = 1, m = 0.1, 2θ0= 30, b = 0.07, λ= 1.1, h/h2= 1.2, and the edge conditions are of the clamped-clamped type.

Electro-elastic results of graphene origami-reinforced sandwich doubly curved shells

Static electroelastic behavior of a doubly curved shell composed of copper core reinforced with graphene origami auxetic metamaterial are studied in the present paper. The shell is subjected to uniform mechanical, electrical and thermal loads. To evaluate effective material properties, the micromechanical models are extended in terms of both material properties of matrix and reinforcement with changes of temperature, volume fraction, folding degree and geometric parameters of graphene nanoplatelets. After extension of energy method using piezoelasticity relations, the governing equations are analytically solved and the then the analytical solution is derived to explore importance of foldability and multifield loading on the responses. After that the comprehensive results are obtained with changes of thermal loading, graphene amount, folding degree, geometric characteristics and foundation’s parameter.

The Impact of Flexural/Torsional Coupling on the Stability of Symmetrical Laminated Plates

In this study, we will evaluate the effect of bending/torsion coupling on the buckling instability and free vibration behavior of symmetrical laminated plates. We will load these plates in-plane with bi-axial or uni-axial, uniform or non-uniform mechanical loads. To quantify this behavior, we’ll compare the results obtained with those of specially orthotropic symmetrical plates (where bending/torsion coupling is absent). A parametric study will be carried out by varying the plate’s aspect ratio, anisotropy ratio and/or lamination angle. The aim of these studies is to construct a planar loading margin for the plate while remaining elastically stable, and to determine a physically admissible limit where we can approximate the behavior of symmetrical laminates to that of specially orthotropic plates (easy to study). We will base ourselves on a Rayleigh-Ritz energy formulation of the problem because of the difficulty of finding closed-form solutions. Following validation of this formulation, a numerical survey of the results will be carried out to quantify the effect of bending/torsion coupling on the instability of this type of plate. Various conditions on the plate boundaries will be used.

Time-harmonic loading over a piezoelectric layered half-space

Mathematical modeling of multilayered piezoelectric (PE) ceramic substantially acquires attention due to its distinctive advantages of fast response time, positioning, optical systems, vibration feedback, and sensors, such as deformation and vibration control. As such, fundamental solution of a PE structure is essential. This paper presents three-dimensional (3D) static and dynamic solutions (i.e. Green’s functions) in a multilayered transversally isotropic (TI) PE layered half-space. The uniform vertical mechanical load, vertical electrical displacement, and horizontal mechanical load are applied on the surface of the structure. The novel Fourier-Bessel series (FBS) system of vector functions (which is computationally more powerful and streamlined) and the dual-variable and position (DVP) method are employed to solve the related boundary-value problem. Two systems of first-order ordinary differential equations (i.e. the LM- and N-types) are obtained in terms of the FBS system of vector functions, with these expansion coefficients being the Love numbers. A recursive relation for the expansion coefficients is established by using DVP method that facilitates the combination of two neighboring layers into a new one and minimizes the computational effort to a great extent. The corresponding physical-domain solutions are acquired by applying the appropriate boundary/interface conditions. Several numerical examples pertaining to static and dynamic response are solved, and the efficiency and accuracy of the proposed solutions are validated with the existing results for the reduced cases. The solutions provided could be beneficial to better developments of PE materials, configurations, fabrication, and applications in the future.

Effect of materials and design on PV cracking under mechanical loading

As the PV industry considers new cell and module designs of lower cost, the reliability and durability become a major issue. Hence, it is important to evaluate the influencing factors on the mechanical strength of solar cells. In this work, a 3D FE model is used to investigate the stresses which are generated from mechanical loading and the XFEM to predict the crack initiation and propagation. Several aspects related to geometric configurations and PV module material properties are investigated. A material imperfection in the form of a locally reduced Elastic modulus by 10% resulted in a decrease of failure load by 70%. PV modules with Si thicknesses of 0.1, 0.15 and 0.2 mm are expected to crack under a uniform mechanical loading of 5400 Pa at different loads. In the case of isotropic Silicon of 0.1 mm thickness, the fracture takes place at a load lower than 2400 Pa. PV modules modelled with isotropic silicon were found to fail at a lower load, approximately by 12%, compared to those with anisotropic silicon. Finally, the study showed that half-cell PV modules experience reduced mechanical stresses, cracking initiates in higher load and the crack propagation is arrested at the boundary of the cell.

Approximate structures of thermoelastic fields induced by a penny-shaped thermal-medium crack in a transversely isotropic layer

It is of practical significance to investigate thermoelastic fields at the front of a penny-shaped crack embedded in a material with finite thickness. The existing works always focus on numerical solutions of the derived integral equations and approximate solutions are seldom studied. In the present study, the problem of a penny-shaped crack in a transversely isotropic layer is addressed under uniform heat flow and mechanical loadings. The extended thermal-medium crack model with a nonlinear relation between heat flow of crack interior and crack opening displacement is used to capture the effect of heat conduction inside crack. The Hankel transform technique is applied to solve governing partial differential equations, then Fredholm integral equations of the second kind are derived. Applying integral kernel series expansion method, approximate solutions to the derived Fredholm integral equations are analyzed and determined. Approximate structures of thermoelastic fields around penny-shaped crack are further obtained. Theoretical analysis and numerical results are carried out to show the applicability of approximate solutions. The observations reveal that the determined approximate solutions have some significance to a practical engineering application. The advantages of the developed methods are to make approximate solutions visible, and some penny-shaped crack problems of thermo-piezoelectric and thermo-magnetoelectroelastic layers could be solved similarly.

Analytical buckling response of sectorial porous plates integrated with piezoelectric layers

This paper is concerned with influence of porosity and mechanical/electrical boundary conditions on buckling of moderately thick, porous sector and annular sector plates integrated with piezoelectric layers. Presence of both porous and piezoelectric elements in a configuration provides new opportunities for manipulating the buckling load broadly. To demonstrate these possibilities, across the thickness of the core plate, varying porosity profiles are considered, yet the network of pores is assumed to be free of fluid. The governing equations of the sandwich plate under uniform in-plane mechanical loading are obtained by taking the Mindlin plate theory and von Kármán assumptions into account; and later the nonlinear nature of the problem is simplified through the use of the adjacent equilibrium criterion. Next, decoupled formulae for all the unknown kinematic variables are reached by introducing two transformation functions. The critical buckling loads are computed analytically by assuming simply supported radial edges and classical boundary conditions for the circumferential edges. Eventually, the effect of the mechanical/electrical boundary conditions, geometrical parameters and porosity is realized by comprehensive parametric studies.

Stress intensity factors for cusp-type crack problem under mechanical and thermal loading

Abstract The general solutions of the stress intensity factors (SIFs) for a cusp-type crack problem under remote uniform mechanical and thermal loads are presented in this work. According to the complex variable theory and the method of conformal mapping, a symmetric airfoil crack is mapped onto a unit circle, and both the temperature and stress potentials are used to solve the relevant boundary-value problems. By introducing the auxiliary function and applying the analytical continuation theorem, the SIFs at the cusp-type crack tip can be analytically determined. The obtained SIF results are dependent on the geometric configurations of the cusp-type crack components and the magnitudes of the mechanical and thermal loads. For some combinations of combined loads, the SIF is maximized, and the system has a high risk of damage.

Numerical deflection and stress prediction of cutout borne damaged composite flat/curved panel structure

This article presents the deflection and stress responses of the concentric cutout impregnated composite curved/flat panel structure, including the variable cutout profiles (square, circular, and elliptical). The model can compute the structural configuration due to the curvature parameter change, i.e., plate, spherical, cylindrical, elliptical, and hyperboloid. The damaged composite structural model is derived using a cubic-order of displacement field kinematics to maintain the stress–strain continuity. The isoparametric type C0 continuous finite element (FE) modeling steps are adopted to solve the structural equilibrium equation of the cutout abided layered composite panels subjected to uniform mechanical loading via an in-house derived MATLAB code. The model accuracy has been established by comparing the deflections and the stresses with the previously published results. Finally, the layered composite shell panel's critical behavior under the static loading has been examined. Different types of numerical problems are solved by varying the associated design constraint parameter, including the cutout relevant factors (shape and size), to show the proposed model applicability.

Three-dimensional fields in an infinite transversely isotropic magneto-electro-elastic space with multiple coplanar penny-shaped cracks

This paper investigates the Mode-I crack problem that a three-dimensional infinite space of transversely isotropic multi-ferroic composite medium is weakened by multiple coplanar penny-shaped cracks under uniform mechanical, electric and magnetic loadings. These cracks are arbitrarily distributed in an isotropic plane of the material. Four kinds of idealized electro-magnetic crack boundary conditions, which assume a crack to be electrically permeable (or impermeable) and magnetically permeable (or impermeable), are adopted, and all the possible combinations of these electro-magnetic crack boundary conditions are considered. An approximate three-dimensional solution of the field variables and expressions of some important fracture mechanics quantities are proposed, by virtue of Kachanov’s method and the generalized potential theory method. Numerical examples for some particular configurations of cracks are presented. Based on a two-crack system, the validity of the present solution is checked by comparing the results with their counterparts from a finite element simulation. Interaction of cracks is investigated as well, by taking the crack size and distance between two cracks as factors. From the phenomena shown in the numerical examples, a reduced solution and an empirical method for evaluating generalized stress intensity factors are proposed.

Buckling behavior of rectangular angle-ply laminated composite plates subjected to thermal and mechanical loads using the meshfree method

This study aims to explore the buckling behavior of rectangular plate with angle-ply overlay under thermal and mechanical loadings using meshless method. The governing differential equations (GDEs) of the plate are based on a new higher-order shear deformation theory (HSDT) and are discretized using polynomial radial basis function (RBF) to cast a set of equations simultaneously. A code is developed for the solution in MATLAB (2019). Uniform temperature differences and mechanical loads are the cause of in-plane loads. Convergence study has been conducted to check the current formulation’s soundness. The accuracy of the contemporary theory and formulation is validated with the published results. A parametric investigation is conducted for buckling behavior under the span-to-thickness ratio, lamination scheme, effect of the number of layers and effect of length-to-width ratio.

Static analysis of multilayer nonlocal strain gradient nanobeam reinforced by carbon nanotubes

This article presents a comprehensive static analysis of simply supported cross-ply carbon nanotubes reinforced composite (CNTRC) laminated nanobeams under various loading profiles. The nonlocal strain gradient constitutive relation is exploited to present the size-dependence of nano-scale. New higher shear deformation beam theory with hyperbolic function is proposed to satisfy the zero-shear effect at boundaries and parabolic variation through the thickness. Carbon nanotubes (CNTs), as the reinforced elements, are distributed through the beam thickness with different distribution functions, which are, uniform distribution (UD-CNTRC), V- distribution (FG-V CNTRC), O- distribution (FG-O CNTRC) and X- distribution (FG-X CNTRC). The equilibrium equations are derived, and Fourier series function are used to solve the obtained differential equation and get the response of nanobeam under uniform, linear or sinusoidal mechanical loadings. Numerical results are obtained to present influences of CNTs reinforcement patterns, composite laminate structure, nonlocal parameter, length scale parameter, geometric parameters on center deflection ad stresses of CNTRC laminated nanobeams. The proposed model is effective in analysis and design of composite structure ranging from macro-scale to nano-scale.

Three-dimensional closed-form solution to elliptical crack problem in magneto-electro-elasticity: Electrically and magnetically induced Maxwell stress boundary condition

An elliptical mode-I crack problem in an infinite multi-ferroic composite material with transverse isotropy under remote uniform mechanical, electric and magnetic loadings is analyzed. The electro-magnetically semi-permeable crack boundary condition and Maxwell stress on the crack faces caused by the electric and magnetic fields are considered, which makes the problem nonlinear. On the basis of the general solution for multi-ferroic composite materials and modern potential theory method, the nonlinear integro-differential boundary equations are established and solved analytically. The field variables in the three-dimensional space and some important fracture mechanics quantities, are obtained in explicit forms. From numerical examples, it is found that the combination of the applied electric and magnetic loadings should be in a elliptical region in the electric displacement-magnetic induction coordinate plane to keep the crack open. Furthermore, in the vicinity of the center of this region, the electro-magnetically semi-permeable crack boundary condition without the Maxwell stress could provide relatively accurate results. Otherwise, the Maxwell stress would have a significant influence, and thus should not be neglected.

Magnetoelastic buckling properties of type-II superconducting thin strip subjected to perpendicular magnetic field and parallel distributed uniform mechanical load

The buckling analyses of type-II superconducting strip under applied perpendicular magnetic field and/or distributed uniform mechanical load are investigated in this paper. Based on the Bean critical state model, the electromagnetic body force is firstly given. Then, based on the classical plate theory and two-point initial value method, the critical buckling states of the superconducting strip with different boundary conditions are analyzed. Numerical results show the effects of both the thickness and boundary conditions of superconducting strip on the corresponding critical buckling loads. The present work should be helpful to the research and application of superconducting thin strips.

Dynamic Bioreactors with Integrated Microfabricated Devices for Mechanobiological Screening.

Biomechanical stimulation is a common strategy to improve the growth, maturation, and function of a variety of engineered tissues. However, identifying optimized biomechanical conditioning protocols is challenging, as cell responses to mechanical stimuli are modulated by other multifactorial microenvironmental cues, including soluble factors and biomaterial properties. Traditional bioreactors lack the throughput necessary for combinatorial testing of cell activity in mechanically stimulated engineered tissues. Microfabricated systems can improve experimental throughput, but often do not provide uniform mechanical loading, are challenging to use, lack robustness, and offer limited amounts of cells and tissue for analysis. To address the need for higher-throughput, combinatorial testing of cell activity in a tissue engineering context, we developed a hybrid approach, in which flexible polydimethylsiloxane microfabricated inserts were designed to simultaneously generate multiple tensile strains when stretched cyclically in a standard dynamic bioreactor. In the embodiment presented in this study, each insert contained an array of 35 dog bone-shaped wells in which cell-seeded microscale hydrogels can be polymerized, with up to eight inserts stretched simultaneously in the bioreactor. Uniformity of the applied strains, both along the length of a microtissue and across multiple microtissues at the same strain level, was confirmed experimentally. In proof-of-principle experiments, the combinatorial effects of dynamic strain, biomaterial stiffness, and transforming growth factor (TGF)-β1 stimulation on myofibroblast differentiation were tested, revealing both known and novel interaction effects and suggesting tissue engineering strategies to regulate myofibroblast activation. This platform is expected to have wide applicability in systematically probing combinations of mechanobiological tissue engineering parameters for desired effects on cell fate and tissue function. Impact Statement In this study, we introduce a dynamic bioreactor system incorporating microfabricated inserts to enable systematic probing of the effects of combinations of mechanobiological parameters on engineered tissues. This novel platform offers the ease of use, robustness, and well-defined mechanical strain stimuli inherent in traditional dynamic bioreactors, but significantly improves throughput (up to 280 microtissues can be tested simultaneously in the embodiment presented in this study). This platform has wide applicability to systematically probe combinations of dynamic mechanical strain, biomaterial properties, biochemical stimulation, and other parameters for desired effects on cell fate and engineered tissue development.

Elliptical crack problem in magneto-electro-thermo-elasticity of transversely isotropic materials: 3D analytical and numerical solutions

Crack problems are of high research value for multi-ferroic composite media, which have great potential in developing multi-functional devices. In account of the magneto-electro-thermo-elastic coupling effect, this paper investigates an elliptical crack contained in an infinite body of transversely isotropic multi-ferroic composite medium. The two crack surfaces are symmetrically loaded by the combinations of uniform mechanical, electric, magnetic and temperature loadings. The electric and magnetic permeabilities of the crack are idealized to be completely permeable (or impermeable), and thus four combinations of boundary conditions are considered. The field variables in the 3D space, as well as some parameters with great significance in fracture mechanics, are derived analytically, with the generalized method of potential theory. A unified solution of the field variables appropriate for all the four cases is proposed. By the principle of virtual displacement, the finite element formulation is also presented. Numerical results obtained from analytical method and simulations are presented for validating the present analytical solutions, and discussing the effect of magneto-electro-thermo-elastic properties.

A screw dislocation near a non-elliptical piezoelectric inhomogeneity with internal uniform electroelastic field

Conformal mapping and analytic continuation are employed to prove the existence of an internal uniform electroelastic field inside a non-elliptical piezoelectric inhomogeneity interacting with a screw dislocation. We focus specifically on the case when the piezoelectric matrix surrounding the inhomogeneity is subjected to uniform remote anti-plane mechanical and in-plane electrical loading and a constraint is imposed between the remote loading and the screw dislocation. The constraint can be expressed in a relatively simple decoupled form by utilizing orthogonality relationships between two corresponding eigenvectors. The internal uniform electroelastic field is found to be independent of the presence of the screw dislocation; moreover, it can be expressed in decoupled form.

Elasticity solution of laminated beams with temperature-dependent material properties under a combination of uniform thermo-load and mechanical loads

An exact solution for simply-supported laminated beams with material properties variable with temperature under a combination of uniform thermo-load and mechanical loads was investigated, based on the two-dimensional (2-D) thermo-elasticity theory. Firstly, the beam was divided into a series of layers with uniform material properties along the interfaces of the beam. The uniform thermo-load acted on each layer was transformed into a combination of the normal surface forces acted at the two ends and the transverse thermo-load. Secondly, the state space method was employed to obtain the general solutions of displacements and stresses in an arbitrary layer. Thirdly, based on the interfacial continuity conditions between adjacent layers, the relations of displacement and stress components between the top and bottom layers of the beam were recursively derived by use of the transfer-matrix method. The unknowns in the solutions can be solved by the mechanical loads acted on the top and bottom surfaces. The convergence of the present solutions was checked. The comparative study of the present solutions with the Timoshenko’s solutions and the finite element (FE) solutions was carried out. The effects of material properties variable with temperature on the thermo-elastic behavior of laminated beams were discussed in detail.

A Nanoscale Hole of Arbitrary Shape with Surface Elasticity

In this paper, we study the plane deformation of an arbitrarily-shaped nanoscale hole subjected to a uniform mechanical load at the infinity. Stress boundary condition along the hole surface is constructed by incorporating the deformation-dependent surface elasticity. The solution is given via the complex variable techniques, including the conformal mapping and series expansion methods. To verify the present formulation, we compare our results for the elliptical holes with those from the literature and observe good agreement between the two sets of results. Then we present numerical examples for four shapes of holes (ellipse, square, pentagon and triangle) with varying sizes to investigate the stress field with surface elasticity. The first aspect we are interested in is what factors can affect the stress field. Our results show that for nanoscale holes with surface elasticity, the stress field can be greatly influenced by the hole size and the hole shape. Specifically, when the hole size decreases, the hoop stress usually decreases, while the normal and shear stresses always increase. However, the hole size hardly influences the stress distribution pattern, which is, in fact, determined by the hole shape. In addition, the hole shape strongly influences the stress magnitude. Another aspect concerned is the positions of the maximum stresses. The results show that for the most cases, the stresses obtain their maximums at a certain corner of the shapes. However, for some shapes, there might be certain stresses that attain their maximums nearby, not at, the corner of the shapes.

Nonlinear bending of third-order shear deformable carbon nanotube/fiber/polymer multiscale laminated composite rectangular plates with different edge supports

The geometrically nonlinear bending behavior of carbon nanotube/fiber/polymer multiscale laminated composite (CNT-FPMLC) rectangular plates with various edge conditions subjected to the uniform transverse mechanical loading is investigated. Based on the Reddy’s third-order shear deformation plate theory and employing the von Karman hypotheses and fundamental lemma of calculus of variations, the governing equilibrium equations including the shear deformation effect and geometrical nonlinearity together with associated boundary conditions are developed. The fiber micromechanics and the Halpin-Tsai relations are employed to approximately calculate the material properties of multiscale composite. Also, the carbon nanotubes (CNTs) are assumed to be distributed uniformly and oriented arbitrarily through the epoxy resin matrix. For the large deflection analysis, first, the generalized differential quadrature (GDQ) method is used to discretize the differential governing equations and corresponding boundary conditions resulting in a set of nonlinear algebraic equations. Then, the pseudo-arclength continuation technique is utilized to numerically solve the resulting nonlinear parameterized equations and subsequently obtain the load-deflection curve of CNT-FPMLC rectangular plates with different edge supports. Several numerical results are provided to reveal the influences of the weight percentage of single-walled and multi-walled CNTs, CNT aspect ratio, volume fraction of fibers, length-to-thickness ratio of plate and boundary conditions on the nonlinear responses of the CNT-FPMLC plates.