Dynamic Response of Laminate Composite Shells with Complex Shape Under Low-Velocity Impact

The present research aims to analyze the response of viscoelastic laminated composite microplate under microparticle low-velocity impact. Hertz contact law is used to model the impact phenomenon between the microparticle and the microplate. According to Kelvin-Voigt theory, the realistic behavior of the structure is considered by considering the viscoelastic properties. The governing equations of the system are derived based on the first-order shear deformation plate theory (FSDT) and the nonlocal strain gradient theory (NSGT) by employing Hamilton's principle. Galerkin's method is employed to solve differential equations of microplate with different boundary conditions. Afterward, the system of time-dependent equations by applying the Newmark' s method is solved. The parametric study is presented to examine the effect of particle radius, particle initial velocity, nonlocal parameter, length scale parameter, viscoelastic modulus, fiber orientation, and different boundary conditions on the impact response of microplate.

Thermoelastic analysis of stiffened sandwich doubly curved plate with FGM core under low velocity impact

Purpose The purpose of this study is to investigate the strain rate effect on the problem of low-velocity impact (LVI) on a beam, including silicon nitride and stainless steel materials. Design/methodology/approach Based on the nonlinear Hertz impact mechanism, the energies related to the impactor and the beam are written, and motion equations are derived using the Lagrangian mechanics and Ritz method. The strain rate term is represented as a damping matrix in the equations of motion. In the issue of LVI on the silicon nitride and stainless steel beam, the effect of internal viscous damping coefficient in simply–simply and clamped–free boundary conditions are studied. Also, the influence of the volume fraction index in the range between zero and one and greater than one on the impact response is investigated. Findings The results make it clear that the strain rate parameter had little effect on the response in LVI. Also, an increase in the volume fraction index has led to a decrease in the contact force and an increase in the rebound velocity of the impactor. Originality/value The effect of strain rate on LVI is theoretically studied in this paper, while in most of the papers, this effect is investigated experimentally and numerically.

The sandwich panel structures with aluminum foam core and metal surfaces have light weight with high performance in dispersing energy. This has led to their widespread use in the absorption of energy. The cell structure of foam core is subjected to plastic deformation in the constant tension level that absorbs a lot of kinetic energy before destruction of the structure. In this research, by making samples of aluminum foam core sandwich panels with aluminum surfaces, experimental tests of low velocity impact by a drop machine are performed for different velocities and weights of projectile on samples of sandwich panels with aluminum foam core with relative density of 18%, 23%, and 27%. The output of device is acceleration‐time diagram which is shown by an accelerometer located on the projectile. From the experimental tests, the effect of weight, velocity and energy of the projectile and density of the foam on the global deformation, and energy decrease rate of projectile have been studied. The results of the experimental testes show that by increasing the density of aluminum foam, the overall impression is reduced and the slop of energy loss of projectile increases. Also by increasing the velocity of the projectile, the energy loss increases. Introduction. Sandwich panels with composite face sheets and foam core are widely used in lightweight constructions, especially in aerospace industries due to their advantages over the conventional structural constructions, such as high specific strengths and stiffness and good weight saving [1]. An early study [2] has indicated that using composite materials instead of aluminium for the face sheets results in higher performance and lower weight. In the meanwhile, as a new multi-functional engineering material, aluminium foam has many useful properties such as low density, high specific stiffness, good impact resistance, high energy absorption capacity, easy to manufacture into complex shape, and good erosion resistance [3, 4], so it is usually used as core material of sandwich panels. However, it has also been found that composite sandwich panels are susceptible to impact damage caused by runway debris, hailstones, dropped tools and so on [2]. The resulting impact damage to the sandwich panel ranges from face sheet indentation to complete perforation, with the strength and reliability of the structures dramatically affected. Unlike for their solid metallic counterparts, making predictions of the effects of low-velocity impact damage are difficult and are still relatively immature. Hence, the behaviour of sandwich structures with aluminium foam core under low-velocity impact has received increasing attention.

Dynamic stability analysis of the sandwich open-type shell on the viscoelastic substrate is presented. The structure is made of one graphene nanoplatelets layer and one piezoelectric layer. To simulate the force pertained to contact between the current impactor and structure, a contact model called Hertz is provided. For obtaining the boundary conditions (BCs) in addition to equations of motion associated with the sandwich open-type shell, first-order shear deformation theory and Hamilton’s principle are utilized to achieve the equations of motion. Then, Galerkin, as well as Newmark approaches, are coupled to solve the equations of the open sandwich-type curved shell subjected to a low-velocity impact. Also, a model employing an adaptively tuned deep neural network (DNN) is developed on the basis of the data of the problem to extract the results. The formulation and solution procedure are verified utilizing other papers. The outcome step has been presented the effect of the impactor’s initial velocity in addition to density on an indentation, absorbed energy, contact force, and indenter speed have been analyzed in detail. Last but not the list, the influence of the impactor’s initial speed and radius on the mode shape of the current structure will be discussed in detail.

In the normal operation of a spherical robot, its spherical shell structure is often accompanied by low velocity impact. At the same time, the spherical shell structure should take into account its protective ability against high strength impact of small probability. Glass fiber reinforced polymer (GFRP), which has high specific strength, specific stiffness, corrosion resistance and an impact energy dissipation coefficient, can be used as the ideal spherical shell material for spherical robots. In this study, the low velocity impact damage of GFRP spherical shell is studied based on the background that a thin-walled shell structure of spherical robot may suffer from large deformation and dynamic load. This study is divided into three aspects: experiment, simulation and calculation. The dynamic response and residual bearing capacity of the GFRP spherical shell is obtained through experiments; the progressive damage model of the composite structure, which demonstrates expounded stress distribution, a structural deformation mode and an energy dissipation mechanism under impact, is established based on the Hashin criterion. Low velocity impact-penetrating failure of the elastic brittle thin-walled GFRP spherical shell is calculated according to the geometrical principle and energy method. In this paper, the material dynamic behavior and impact damage of a GFRP spherical shell are systematically studied. This is of great significance for the development of high-performance spherical robots and the realization of accurate control.

In the present study, oblique low-velocity impact (OLVI) on GLARE fiber-metal laminates (FMLs) has been modeled using finite element analysis (FEA) for the first time. Two types of boundary conditions (BCs) can be considered for impactor in the low-velocity impact: constrained (if the impact angle between the impactor and target remains constant during and after the contact) and free (if rotation of the impactor and change in angle with respect to the target is likely) BCs. The more details of these BCs are described in the paper. The OLVI is numerically modeled for four different impact angles. Effect of BC types and impact angle on energy absorption, as well as maximum contact force, is investigated. Due to lack of experimental results for the OLVI on FMLs in the open literature, the authors had to validate the present modelling via the experimental data of the perpendicular low-velocity impact. An excellent agreement was obtained between the numerical results and the experimental data. The results of present study reveal that at the same impact angle, the maximum contact force and energy absorption are greater for the constraint oblique impact (Constrained OLVI). In addition, in the Constrained OLVI, the maximum energy absorption occurs at larger impact angles, while this occurs at smaller impact angles for free oblique impact (Free OLVI). The conclusion to be drawn from all of the cases studied in this paper is that the maximum contact force occurs in the Constrained OLVI with smaller impact angles. Moreover, the maximum energy absorption takes place in the Constrained OLVI at higher impact angles.

In Memoriam: Dr. Clive L. Dym (1942–2016)

Composite Materials are being used increasingly in aircraft structures due to their high specific strength and stiffness, and the resultant weight savings. Traditionally, the use of graphite fiber-reinforced composites have been confined to secondary structures. However, requirements for reduced structural weight, improved aircraft performance, and efficiency are making the composite materials increasingly competitive for expanded usage in the primary, load carrying structures. In comparison to conventional metals, an understanding of the complex behavior of composites is still in its infant stage, and applications are based on knowledge gained through extensive experimental programs. Past experiences and experiments have confirmed that the graphite fiber-reinforced composite laminates have low ultimate strains, no plastic deformation range, and no usable strength in the thickness direction. These limitations become very obvious when laminates are subjected to impact loads. In this paper, the effect of low-velocity impact damage on the compressive strength of composite laminates is addressed. Due to the low-velocity impact loading laminates suffer an extensive internal damage such as delaminations and the damage on the back surface known as spalling. Therefore the study of impact damage susceptibility of these composite laminates is increasingly important. While considerable experimental and analytical studies have been made on the low velocity impact phenomenon, an experimental understanding of the progressive damage mechanics and its effect on the compressive strength is not fully known. In the experimental program, 16 ply, 32 ply and 48 ply laminated graphite/epoxy composite plates with quasi-isotropic lay up were tested for two different types of loading conditions, the first one was low velocity impact loads, and the second one was equivalent quasi-static loads. In both cases the laminates were held in a NASA designed steel fixture, which simulated the simply supported boundary conditions. The impactor tip area and weight of the impactor was kept constant for all the tests, and tests were performed using Dynatup low velocity impact testing facility. Preliminary impact tests were performed to establish the lower bound (incipient damage) and upper bound (visible back face damage, spalling) energy levels for each 16 ply, 32 ply and 48 ply laminates. Seven energy levels, first with 20 % below the lower bound, second and seventh lower and upper bounds, and third through sixth in between lower and upper bounds with an increment of 20 % were chosen to generate the progressive damage data for laminated composite plates of varying thickness subjected to low velocity impact loads. In addition to the impact tests, laminated plates were subjected to quasi-static loads which simulated low velocity impact loads. Both the static and impact tested laminates were C-Scanned to identify the internal damages.

Simulation of the dynamic response of GLARE plates subjected to low velocity impact using a linearized spring–mass model

ABSTRACTThermal buckling and vibration of functionally graded (FG) sinusoidal microbeams with temperature-dependent properties and three kinds of temperature distributions are investigated in this article. As one material length scale is introduced, the modified couple stress theory is capable of predicting the small-scale effects. Material properties of FG microbeams are calculated using the Mori–Tanaka method. Furthermore, temperature-dependent properties are taken into account to investigate the mechanical characteristics of FG microbeams in high–thermal-gradient environment. Motion equations and the associated boundary conditions are obtained simultaneously through variational principle. Then Navier procedure and the differential quadrature method incorporating an iterative procedure are used to solve the governing differential equations with temperature-dependent properties and general boundary conditions. Numerical examples are performed for demonstrating the influences of temperature distribution, beam thickness, material length scale, slenderness ratio, shear deformation, functionally graded index, boundary conditions, and temperature-dependent/independent properties on thermal buckling and free vibration behaviors of FG microbeams.

The objective of the present paper is to study the effect of porosity on vibration and buckling responses for sandwich plate supported with different boundary conditions at the edges. The formulation is performed for recently developed sandwich plate using new modified sigmoid function based functionally graded material plate of different symmetric and asymmetric configurations. Three different types of porosity are considered viz. even, uneven but symmetric, and uneven but non-symmetric. A new uneven non-symmetric porosity model is used in which micro-voids are varied in accordance with material property variation in the thickness direction in order to capture the accurate distribution of voids on the plate. The variational principle is employed to derive equilibrium equations. A closed form solution is obtained using the assumed solution with shape functions satisfying the edge boundary conditions using Galerkin Vlasov’s method. Free vibration and buckling analysis have been performed to study the effect of porosity, geometric configurations, inhomogeneity parameter, and buckling load parameter. These studies are performed on sandwich sigmoid function based functionally graded material plate for different boundary conditions and plate configurations. It is observed that in several cases with uneven symmetric porosity (P-2) distribution, the reduction in effective inertia appears to be more prominent in comparison to the reduction in effective stiffness of the plate and uneven non-symmetric porosity (P-3) distribution ascertains the realistic idealization for a plate with micro-voids. The higher modes of vibrations and nature of in-plane load are very sensitive to the type of porosity distribution considered. In addition, zero frequency parameter and zero critical buckling load in a load frequency curves correspond to critical buckling load and frequency parameter, respectively. The accuracy and validation of the present formulation are determined by considering different examples.

Summary This work addresses the development of some alternative hybrid and mixed variational formulations for the geometrically-exact three-dimensional first-order-shear shell boundary value problem [1,2]. In the framework of the complementaryenergy-based formulations, a Legendre transformation is used to introduce the complementary energy density in the variational statements as a function of the cross-sectional resultants only. The corresponding variational principles are shown to feature stationarity within the framework of the boundary-value-problem. The main features of the principles are highlighted, giving special attention to their relationships from both theoretical and numerical point of view. Variational principles constitute the core of the development of numerical methods in Solid Mechanics. The utility of such principles is two-fold: first, they provide a very convenient method for the derivation of the governing equations and natural boundary conditions of the boundary value problem and, second, they provide the mathematical foundation required to produce consistent numerical approximations. In this second role, the variational methods have been most useful in Computational Solid Mechanics [3]. Many different variational principles can be constructed depending on the equations enforced in the weak form. Perhaps the most remarkable variational principle is the Principle of Stationary Total Potential Energy, which states that, among all kinematically admissible displacement fields, those that satisfy the equilibrium conditions in the domain and at the boundary, lead to a stationary value of the total potential energy functional. In this paper, after the presentation of many mixed variational principles for the nonlinear analysis of shells, we derive a hybrid form of the Two-field Principle of Total Complementary Potential Energy, which is used on a totally consistent derivation of equilibrated co-rotational finite elements [4].

On the dynamic response of an orthotropic finite cylindrical shell to an arbitrary pressure field

Large displacement transient analysis of FGM super-elliptic shells using GDQ method