Central Deflection Research Articles

On resonance behavior of sandwich conical shell

Forced vibration is one of the essential behaviors of structures to predict the mechanical properties of various systems. Magneto-rheological (MR) or electro-rheological (ER) materials, due to many possible control-based applications, have gotten much attention in the oscillating system. Thus, in the present work, for the first time, the forced vibration of a conical shell made of three layers with an electrorheological (ER) core and reinforced composite with GPLs is investigated. The formulations are derived from the principle of Hamilton. With the aid of compatibility equations, the interfaces between the core and composite face sheets are simulated. The coupled hyperbolic differential quadrature method (HDQM) and Runge-Kutta solution procedure is employed to solve the coupled governing equations of the current system. The computational method’s accuracy is confirmed by comparing computed results with those available in the literature. The results show that the number, weight fraction, thickness, and pattern of composite layers, electric/magnetic field, and geometry of the conical panel have an important role in the central deflection and phase plot of the current sandwich structure.

A rate-dependent peridynamic model of reinforced concrete subjected to explosive loading

Explosive loads caused by various factors seriously threaten the security of reinforced concrete (RC) structures. To explore the dynamic damage and failure patterns of RC structures under explosive loads, new rate-dependent peridynamic (PD) models for concrete and reinforcement are proposed. For concrete, the behavior of progressive damage and the compressive deformation limit are also taken into account. The ideal microplastic PD model is adopted for reinforcement. Then, this paper investigated the failure process of RC slabs under close-in explosive loads and obtained crack propagation paths and central bending deflections consistent with the test results. The results manifest the established PD model can correctly calculate the damage process of RC structures under explosive conditions.

Analysis of Lens Surface Shape Based on Theory of Plates and Shells

The purpose of this article is to improve the accuracy and expand the force analysis of the lens by using the theory of plates and shells and reciprocal theorem. The first one concerns the deflection expression of a circular lens of equal thickness supported at several uniform points. The second calculates the deflection of the lens under its own weight, and then starting from known Zernike coefficient, PV value and RMS value in optics, the first 37 Zernike coefficients are obtained. The third compares the Zernike coefficients and lens center deflections of partic-ular cases. The derivation process based on plates and shells theory and reciprocal theorem is given in details. As validation, the lens deflec-tion expression is applied to calculate 4 points support, the predicted re-sults illustrate great agreements with the finite element simulation solution. Finally, the proposed method has shown great potential for engi-neering analysis and may also bring inspirations for optical field, as well as other plate and shell theory system.

Ballistic prediction of ceramic armor backed by thin metal plate against threats of small and medium‐calibers

AbstractBased on the principle of energy balance, a new analytical model is established to estimate the ballistic performance of ceramic‐faced armor against small and medium‐caliber projectiles. The energy consumption of ceramic is described as the product of compressive strength and erosion volume of ceramic. Despite its simple form, it represents the main response characteristic of ceramic erosion. Moreover, considering the dependence of the fracture cone half‐angle on the ceramic/metal thickness ratio and projectile velocity, one has innovatively incorporated them in the present model to predict reasonably the half‐angle evolution. To further simplify the analytical calculation and facilitate its application, an explicit prediction formula of the central deflection on thin metal plate is adopted. Then, the accuracy of analytical prediction has been carefully checked with the ballistic test data of small and medium‐caliber projectiles to penetrate light ceramic‐faced armor. The satisfactory consistency between the experimental and analytical results has confirmed the validity of the present model. It is therefore expected to be a powerful tool for the optimal design of new ceramic‐faced armor.

Nonlinear free vibration of bi-directional functionally graded porous plates

Understanding the nonlinear behavior of advanced engineering structures is of great importance in supporting the analysis, design, and manufacturing processes. The primary objective of this paper, therefore, is to focus on exploring the nonlinear free vibrational characteristics of bi-directional functionally graded (FG) plates considering internal pores under various conditions. To accomplish this, we present an approximate numerical model derived based on the framework of NURBS-based isogeometric analysis (IGA), in conjunction with four-variable refined plate theory (RPT) and the von Kármán assumption, to reckon the displacement field. The mechanical properties of bi-directional FG plate models can smoothly and continuously vary along two in-plane directions according to a power law. Additionally, it is assumed that internal porosities in the matrix materials can be dispersed into two independent patterns, either the even or uneven porosity distributions. The nonlinearity in free vibration, assessed by means of the nonlinear-to-linear frequency ratio related to the central deflection amplitude, can be obtained using an iterative scheme with a displacement control strategy. The accuracy and effectiveness of the current numerical model are demonstrated through a comparison with existing solutions. Comprehensive parametric investigations are subsequently carried out to provide insight into the impact of various factors on the nonlinear free vibration characteristics of plate structures under different conditions. The new insights obtained from this research could serve as valuable benchmark outcomes as well as contribute to a more comprehensive understanding of the nonlinear responses in future analysis and design processes.

Bending and buckling analysis of functionally graded graphene origami metamaterial irregular plates using generalized finite difference method

Bending and buckling behavior of graphene origami(GOri) metamaterial irregular plates (octagonal star plates, cordiform plates, a quarter of annular plates and a quarter of annular plates with a hole) under different boundary conditions are investigated based on the higher-order shear deformation theory. The metamaterial by adding GOri to copper matrix in the form of gradient arrangement as reinforcement material has the properties of negative Poisson's ratio (NPR) and compressive, flexural as well as fracture toughness beyond traditional materials that are independent of the topology/architecture of the structure. The governing equations of irregular plate structures are deduced with Hamilton’s principle. Generalized finite difference method, which is a meshless method based on Taylor series expansion and moving least squares approximation, is adopted to solve the numerical solutions. The accuracy and convergence of the proposed method are verified by numerical examples. Numerical experiments show that with the increase of GOri weight fraction, the central bending deflection of irregular plate structures decreases as the folding degree of GOri rises from 20% to 80% and the temperature changes from 300 K to 400 K, the opposite conclusions can be drawn for the buckling. The research on the bending and buckling behavior of irregular plate structures in this paper has important theoretical value for its future application in aerospace engineering field.

Impact Response Analysis on Orthogrid Stiffened Composite Sandwich Plates Embedded with Viscoelastic Material Considering Temperature and Moisture Effects

In this work, a new composite sandwich plate including a viscoelastic material (VEM) filling orthogrid core is proposed. Taking temperature and moisture effects into consideration, the dynamic ‘analysis for impact responses of this structure is presented. The equivalent material properties of the composite core layer are calculated using the Halpin–Tsai model. In order to model the impact force between the impactor and the structure, the modified Hertz contact law is utilized. The governing equations of the structure are derived by employing the Reddy’s higher-order shear deformation theory (HSDT) and Hamilton’s principle. Then the governing equations are solved through the Galerkin method with the aid of the Newmark direct integration scheme. After verifying the reliability and accuracy of this model, the effects of temperature, moisture, initial velocity of the impactor and boundary condition on the contact force and central deflection of the structure are discussed in detail. It has been demonstrated that changes of environmental temperature and moisture play a significant effect on the damping characteristics and impact responses of the composite sandwich plates.

Natural element hierarchical models for static and free vibration analysis of cylindrical panels

Most of studies on the hierarchical models were restricted to beam- and plate-like structures using the finite element method. In this context, this study intends to present the hierarchical models for cylindrical panels and investigate their characteristics using 2-D natural element method (NEM). The displacement field of cylindrical panel is decomposed into the triple-vectored in-plane functions and the assumed thickness polynomials, and the hierarchical models are defined by sequentially increasing the maximum orders of thickness polynomials from (1,1,0). The triple-vectored in-plane functions are approximated by applying 2-D NEM to the unfolded rectangular plane of curved mid-surface of cylindrical panels, for which the stiffness matrices corresponding to the membrane and transverse strains and stresses are calculated using the selectively reduced integration technique to avoid shear-membrane locking. The hierarchical models are demonstrated and validated from the comparative numerical experiments of bending and free vibration of cylindrical panels. The present hierarchical models provide the central deflections and the natural frequencies which are in good agreement with the reference solutions. In addition, the characteristics of hierarchical models such as the limit property and the modeling and approximation errors are investigated with respect to the model level and the width-thickness ratio and the grid density. It is found that the hierarchical models show the locking-free robust and spectral variation in the central deflection and natural frequencies.

Nonlinear Behavior of Fgm Skew Plates Under In-Plane Load

Nonlinear behavior of Functionally Graded Material (FGM) skew plates under in-plane load is investigated here using a shear deformable eight noded iso-parametric plate bending finite element. The material is graded in the thickness direction according to a power-law distribution in terms of volume fractions of the constituents. The effective material properties are estimated using Mori-Tanaka homogenization method. The nonlinear governing equations for the FGM plate under in-plane load are solved by Newton-Raphson technique to obtain the out-of-plane central deflection and in-plane displacement of the loaded edge. The existence of bifurcation-type of buckling for FGM plates is examined for different boundary conditions, constituent gradient index, and skew angle.

Finite Element-Based Free Vibration and Deflection Analysis of Bio-Composites Hybrid Laminated Skew Plates Using Experimental Elastic Properties

In this study, the frequency and deflection response analysis of basalt, soy, flax and hybrid pineapple and flax hybrid laminated skew plates are done. The conventional hand-layup method is used to fabricate the different bio-composites-based laminated structures. The uniaxial tension test is conducted in the INSTRON 5967 UTM to determine the elastic properties of the bio-composite laminated structure as per ISO 527-5 standards. The hybrid laminate skew plate is modeled using the first-order shear deformation theory (FSDT) and their elastic properties are obtained from the uniaxial tensile test from which the frequency and deflection of the skew laminated plates are calculated. The eight-noded shell elements (S8R5) with each node having five degrees-of-freedom are deputed in the commercial finite element method (FEM) package ABAQUS to beget the numerical solutions. The damping effect is neglected in the analysis. The accuracy of the proposed model is verified with available literature and found to be in good agreement. Later, the effect of different parameters such as boundary conditions, aspect ratio and skew angles on the natural frequency and deflection of the bio-composites hybrid laminated skew plates are investigated. The obtained results inferred the natural frequencies are decreasing with an increasing aspect ratio of skew plates. The skew angles help to increase the natural frequencies of skew plates. The central deflections are lower for high-skew angled laminated plates.

Large Deflection Analysis of Rhombic Sandwich Plates with Orthotropic Core

This paper represents nonlinear analysis of rhombic sandwich plates with orthotropic core under uniform load. Banerjee’s hypothesis [1] involving a new form of energy expression in the total potential energy of the system has been employed. As a consequence the differential equation is decoupled keeping intact its nonlinear character. The aim of the present study is to analyze the nonlinear behaviour of rhombic sandwich plates with orthotropic core under uniform load for different skew angles. The results have been obtained both for movable and immovable edges from a single cubic equation. Numerical results (central deflection vs. load) have been computed and compared with known results for square sandwich plates only. Results for different skew angles are believed to be new.

Thermal Postbuckling Analysis of Thin Uniform Square Plates On Winkler Foundation - Effect of Use of Green’s Strain-Displacement Relations

A new simple formulation is developed in this paper, to predict the realistic thermal postbuckling behavior of the square plates, on Winkler foundation. If the plate is subjected to a uniform temperature rise, and also undergoes large deflections, mechanical equivalent inplane compressive, and tensile loads are developed, with the condition of the inplane immovability of the normal edge displacements of the plate. The nature of the distribution of these inplane compressive and tensile loads are similar, but have different magnitudes, which act along the x- and y- directions of the plate. The use of the Green’s nonlinear strain-displacements relations, which do not impose any restriction on the magnitude of the large deflections, to predict the realistic thermal postbuckling loads. The thermal postbuckling results of the plates obtained from this formulation, are validated indirectly, as the corresponding results are not available in the literature, with those of the columns without the elastic foundation. For the non-zero values of the foundation parameter, the present numerical results of the plates, with respect to the central deflection, show the proper physical trends of the nonlinearity, and demonstrate the simplicity of the present formulation.

An Investigation of Thermal Postbuckling of Uniform Columns on Variable Winkler Foundation by Using Rayleigh-Ritz and Heuristic Formulations

An investigation of the two different formulations, to predict the thermal buckling and postbuckling behavior of uniform hinged-hinged and clamped-clamped columns on the elastic variable Winkler foundations, is presented in this paper. The first one is the Rayleigh-Ritz and the second one is relatively simple heuristic formulation. Though the effect of the uniform Winkler foundation is thoroughly studied for the columns and other structural members, the variable Winkler foundation is not received much attention by the researchers. In the present investigation, two types of variable Winkler foundations, wherein the first and second terms of the foundations contain a constant and the variable parts, which varies with two types of sine functions, are considered. It is shown that the expressions obtained from the two formulations, for the ratios of the thermal postbuckling to the buckling load parameters are, not only the same but also validate the results, for the specified values of the central deflection and foundation stiffness parameters. A comprehensive set of numerical results are presented in this investigation, to obtain the thermal postbuckling behavior of uniform hinged-hinged and clamped-clamped columns on the variable Winkler foundations.

Effect of Fire Flame (High Temperature) on the Self Compacted Concrete (SCC) One Way Slabs

Experimental work was carried out to investigate the effect of fire flame (high temperature) on specimens of one way slabs using Self Compacted Concrete (SCC). By using furnace manufactured for this purpose, twenty one reinforced concrete slab specimens were exposed to direct fire flame. All of specimens have the same dimensions. The slab specimens were cooled in two types, gradually by left them in the air and suddenly by using water. After that the specimens were tested under two point loads, to study, the effect of different: temperature levels (300ºC, 500ºC and 700ºC), and cooling rate (gradually and sudden cooling conditions) on the concrete compressive strength, modulus of rupture, flexural strength and the behavior of reinforced concrete slab specimens and comparing the results with specimens without burning (reference specimens). The results showed that, the concrete compressive strength, concrete modulus of rupture and the flexural strength decreases while the maximum (central) deflection increases with increasing the fire flame temperature. For suddenly cooled specimens the residual flexural strength is less than that of gradually cooled specimens while the deflection is greater. For slabs with 20 MPa concrete strength and gradually cooled, the residual bending strength percent is 81.5%, 75% and 62.3% ,while the increase in central deflection is 5%, 33%, and 105% at burning temperature 300ºC, 500ºC and 700ºC respectively. For suddenly cooled specimens of the same strength and exposed to the same temperatures above the residual flexural strength is 77.9%, 68.3% and 58.3% while the increase in central deflection is 25%, 52%, and 118% respectively. When the strength of concrete specimens increase, the residual flexural strength experiences small increase and the increase is of lower rate in the central deflection for 300 ºC and 500 ºC burn temperatures while the decrease is significant for 700 ºC burning temperature.

Structural design and flow field characteristics analysis of a new spin-on multi-hole jet drill bit for radial horizontal wells

In order to improve the rock breaking and drilling capacity of the jet bit in radial drilling, a new spin-type multi-hole jet bit was designed. The RNG K-ε turbulence model is used to analyze the flow characteristics of the internal and external flow fields of the designed jet bit, and the influence of the rotational speed and nozzle distribution on the flow field characteristics of the jet bit is analyzed to provide a basis for the design and structural parameter optimisation of the jet bit in radial horizontal wells. The results show that the internal flow field of the jet bit can be divided into four zones: the forward jet zone, the bottomhole overflow zone, the reverse overflow zone and the low-speed reverse flow zone. The reverse jet consists of six straight jets uniformly distributed along the circumferential direction and arranged at equal angles around the axis of the rotating body in the flow field. The reverse jet also impinges on the well wall to form an overflow zone, which provides self-propulsion and acts as a reaming agent. As the injection distance increases, the axial velocity rapidly decreases to zero and the decay velocity of the three groups of jets gradually approaches at the impact wall. Rotational speed has an effect on the decay of the flow velocity at the centre of the forward jet axis. When the angle of inclination is very small, the rotational speed has almost no effect on the decay of the axial velocity of the jet. The greater the angle of inclination, the greater the linear angular velocity at the jet exit, the more the jet mixes with the surrounding crossflow, the faster the dissipation of jet energy and the faster the jet decays along the axis. Controlling the magnitude of the rotational speed has to be taken into account in the design. Initially, the optimum values of the different structural parameters were determined as the central nozzle coinciding with the drill axis, the central forward nozzle deflection angle of 20°, the external nozzle deflection angle of 20° and the external nozzle tension angle of 15°.

Accurate solutions of a thin rectangular plate deflection under large uniform loading

The large deflection of a thin rectangular plate under uniform loading is a classic problem in solid mechanics. However, the equations are challenging to solve due to their strong nonlinearity. To the author’s best knowledge, existing studies have only reported solutions for rectangular plates with immovable clamped edges within the range of loadings a4q/(Dh)<500. In this study, we employ the homotopy analysis method (HAM) to address this problem and obtain accurate solutions even when the loading a4q/(Dh) reaches as high as 105. Additionally, we discover that the central deflection w(0,0)/h follows a scaling law of [a4q/(Dh)]1/3 for loadings a4q/(Dh)>104, which agrees with the scaling law for extremely large deflections. Consequently, we can utilize this scaling law to extrapolate our homotopy series solution from a4q/(Dh)=104 to even larger loadings. Our investigation also reveals that the bending and membrane stresses increase with the loading. The maximum bending stress is located at the edge, while the location of the maximum membrane stress shifts from the plate center towards the edge as the loading increases. Moreover, we find that even for large deflections, the bending stress remains significant at the edge, challenging the assumption of negligible bending stress adopted by the membrane equations. Thus, the membrane equation may over-predict the plate deflection even under large loadings. These findings advance our understanding of the large deflection of a thin rectangular plate with clamped edges, which has important applications in aerospace, ocean, chemical, and microelectronic engineering. The results presented in this paper can also be used to verify other algorithms designed for highly nonlinear problems.

Effect of the yaw angle on the aerodynamics of two tandem wind turbines by considering a dual-rotor wind turbine in front

The innovative dual-rotor counter-rotating wind turbine (CRWT) shows great importance in the development of offshore wind farms. In this paper, the performance and wake characteristics of the independent CRWT and two tandem wind turbines equipped with a CRWT at different yaw angles were numerically studied using the open-source software SOWFA (Simulator fOr Wind Farm Applications). The actuator line model (ALM) and large-eddy simulation (LES) were used to model wind turbines and turbulent flows. The third generation of vortex identification criterion was used to analyze wake vortex characteristics. The results indicated the auxiliary rotor had a negligible effect on the main rotor in terms of the dominant frequency and fluctuations. In comparison with the rotational blade frequency (BF), it was found that one BF and double BF were equivalent to the dominant frequency of the SRWT and CRWT, respectively. The CRWT suffers a greater velocity deficit and has a faster velocity recovery. In the case of tandem wind turbines, the upstream wind turbine equipped with a CRWT performs minimal influence on the optimal yaw angle of 30°. In addition, the effects of the yaw angle on wake center deflection, wake width, and performance fluctuation for the downstream wind turbine were investigated.

Bending properties of carbon fiber reinforced composite multilayer damping structures with different types of stiffeners

Carbon fiber reinforced composite multilayer damping structures with different types of stiffeners demonstrate excellent mechanical properties. This paper deals with the bending properties analysis of carbon fiber reinforced composite multilayer damping structures with different types of stiffeners for the first time. A theoretical model was constructed to investigate the bending performance of the structure under static loading based on structural stress transfer mechanism between stiffener and composite plate. Moreover, the theoretical solution was compared with the numerical simulation results to confirm their validity. Finally, structural parameters were considered to discuss the change law of the structural center deflection.

Miniaturization and modeling of a folded beam-based microelectromechanical intraocular pressure sensor

This paper describes the design and detailed analysis of a microelectromechanical system (MEMS) capacitive pressure sensor consisting of nested folded beam suspensions and variously shaped diaphragms that can be used as a part of an LC tank implant circuit for biomedical pressure sensing applications, designed specifically for continuous intraocular pressure (IOP) monitoring in glaucoma patients. The pressure sensor has been designed to measure pressures within the IOP sensor range of 0–8000 Pa. This paper aims to reduce the size of the sensor in comparison to previous research. Significant benefits of miniaturization include requiring less energy, being lightweight, being inexpensive, and having minimal impact on the objects being detected. The MEMS implantable pressure sensor for continuous monitoring of IOP would prevent the progression of the disease, and these tiny devices could alleviate patients’ suffering. Microbeams are likely the most widely utilized structural element in MEMS. This design adds nested folded beam suspensions to the diaphragm, which reduces the diaphragm’s residual tension and rigidity; as a result, the device’s dimension is smaller than the diaphragm without flexible beams (previous work). Due to the reduced rigidity, nested folded beam suspensions can also enhance sensitivity. Finally, the central deflection of the diaphragm will be determined under uniform external pressure. Using COMSOL/Multiphysics and SolidWorks, the design and simulation of pressure sensors have been accomplished. The outcomes reveal that the capacitive pressure sensor with nested folded beam suspensions and the rectangular diaphragm is better suited for measuring IOP, and its dimensions are also smaller than those of previous works ().

Design and analysis of lightweight stiffened honeycomb metallic sandwich panels under high-intensity air blast

An explosive attack on a vehicle can cause catastrophic damage, injury, and loss of life. Experimentally evaluating the blast performance is very costly, hazardous, and environmentally polluting. The numerical investigation of blast behavior is a good alternative. However, this numerical study showed an effort toward improving metallic sandwich panels’ ability to withstand explosion loads of 1–3 kg of TNT at a distance of 100 mm. The blast mitigation of square and circular tube honeycomb cores was compared. The foam and circular tube stiffeners were used to optimize the honeycomb sandwiches’ blast mitigation characteristics. Radial face deflection, face center deflection, core crushing behavior, internal energy, and plastic dissipation energy parameters were used for the characterization of blast behavior. The obtained results indicate that the circular tube honeycomb has better blast mitigation characteristics than the square honeycomb, which improves with foam filling. The circular tube-strengthened square honeycomb provides the lightest stiffened sandwich panel with the smallest deformation and face deflections under all explosive loadings.