Equivalent Solid Plate Research Articles

Experimental study on the synergetic damage of sandwich panel with armored hybrid core under combined blast and fragment loading

Synergetic damage under combined blast and fragment loading drives innovational design of protective structures. In present study, sandwich panel with armored hybrid core was designed, fabricated and finally tested under combined blast and fragment loading. The failure behaviors and the underlying mechanisms were analyzed for the components of sandwich panel. The sandwich panel displayed superior performance over equivalent solid plate. The designability of special interest was exploited by elaborating the effects of face sheet configuration, core material and core sequence on the failure behaviors. Experimental results demonstrate that the same thickness of the front and back faces is beneficial for the constraint of back face deflection. The aluminum foam and ultra-high molecular weight polyethylene (UHMWPE) laminate, adopted as the components of armored hybrid core, cooperated well against combined blast and fragment loading by suffering crushing erosion failure and global bulge deformation, respectively. The potential of armored hybrid core is strongly associated with the core sequence. The ceramic layer supported by the material with high stiffness and the protection of upper bulletproof material for UHMWPE laminate layer would benefit the performance of whole panel. The optimal design of core sequence could markedly reduce back face deflection and even avoid the petalling failure of back face.

Dual-mechanism auxetic-core protective sandwich structure under blast loading

This paper introduces a protective sandwich structure with simultaneous auxetic compression and tension behaviour (termed as the dual-mechanism) in the core. To achieve the proposed mechanism, a novel architected cellular structure, named as the dual-mechanism auxetic (DMA), was developed. The protective performance of the DMA was examined by subjecting the DMA-core sandwich panel (DMASP) to blast loading through computational modelling. A series of dynamic numerical models were developed in LS-DYNA, and validated with the past experimental results. The protective performance of the DMASP was evaluated comprehensively based on energy absorption, stress mitigation, and deflection control. Moreover, the protective performance of the DMASP was compared with an equivalent areal density solid plate. In addition, parametric studies were conducted to investigate effects of various design parameters and explosive environments on the protective efficacy of the DMASP. The numerical simulations uncovered that, in addition to high energy absorption capacity of the DMA core, the dual-mechanism was beneficial to mitigate high stress transfer to the protected structure by redirecting stress in the lateral direction through auxetic tensile behaviour. Furthermore, the DMASP offered better protective performance than the equivalent solid structure with respect to all the evaluation criteria under different blast loading scenarios.

Bending Analysis of Molded Composite Grating Panels: Theoretical and Experimental Investigations

Proposing a theoretical procedure, the lattice structure of a composite grating is replaced with an equivalent orthotropic homogenous plate. Accordingly, the bending analysis of molded grating panels is facilitated using plate-bending theory as a manual calculation. The homogenization method establishes the required analytical relations for estimating effective material properties and effective thickness of the equivalent solid panel. The bending tests are performed on manufactured molded composite gratings under concentrated and distributed loadings. The performed test is also numerically simulated using finite element method. The results of developed theoretical modeling and finite element analysis are compared with experimental observations. A very good agreement is observed between the conducted experiments and estimated results through either numerical or theoretical modeling. Moreover, the performance of the theoretical modeling is also examined for other types of loadings and constraints and the outputs of the developed modeling are compared with available experimental data in open literature. The promising ability of proposed modeling procedure in replacing grating panels with equivalent solid plate is demonstrated for different meshes. This capability enables the engineers to perform bending analysis of grating panels with different meshes very easily and rapidly.

Analytical Study of Operational Properties of a Plate Shock Absorber of a Sucker-Rod String

Sucker-rod pump plant operation is accompanied by inertial and shock loads, affecting the fatigue strength of sucker rods and causing possible accidents. This work proposes the original design of a shock absorber of a sucker-rod string. The peculiarity of the proposed design is the usage of thin plate packages as a bearing elastic element of the shock absorber. This approach to the elastic element’ design provides the shock absorber to be easy to manufacture and operate. Sucker-rod string protection from extra load will increase the sucker-rod pump plant efficiency in general. This study aims at developing shock absorber’s design and studying its most important performance options—strength and rigidity. A mechanical and mathematical model of a shock absorber’s elastic element was developed in order to specify its deformation. A package of thin plates was modelled as an equivalent solid plate with a cylindrical rigidity providing equal properties of the solid model and the plate package. This model makes possible to describe analytically the stress-strain state of the shock absorber bearing elements. The work presents the final expressions of the shock absorber’s strength and rigidity assessing in a convenient form for engineering practice. The numerical approbation of the obtained analytical results was carried out as the case of a plate elastic element. The authors give recommendation on the bearing unit’s design of the shock absorber.

Iterative Weight Reduction Process

In this article, iterative process for weight reduction was used by applying the design for manufacture and assembly process and FEM calculations. This study presents a successful development case of an oil sump structure of a large ship engine. Main structural modification was the transition from plate steel structures to sheet metal based panel structure. As a result of the iterative process, the weight of the developed oil sump was 40% lighter, and the natural frequencies were significantly increased. The study showed that the process allows designing the final product without massive prototyping. 1. Introduction There are several different core types for corrugated panels, for example, the X-profile, tube, Z-profile, hat-profile, and V-profile. The V-profile may need some special equipment for manufacturing and the profile is typically used for the lightest panels. Commercial availability of the hat-profile is better and the quality is often accurate enough for laser welding (Kujala & Klanac 2005). Laser welding is more challenging for V-profiles. In numerous applications, these metallic panels have shown very promising commercial possibilities due to excellent mechanical properties (Liang et al. 2001; Tian & Lu 2005; Zhang et al. 2015), but still there is a lack of public studies dealing with actual applications using good properties of the metallic sandwich panels for commercial solutions. Several research studies have been published in recent years on the analysis of metallic corrugated-core sandwich panels for strength, vibration control, noise control, and blast resistance. For example, Valdevit et al. (2006) noticed that buckling loads are hard to predict with Finite Element (FE)-simulations, but it is more suitable for limit loads. Zhang et al. (2015) investigated the dynamic responses of sandwich panels with triangular corrugated cores under air blast load. They noticed that sandwich plates suffered smaller back face deflections than equivalent solid plates at low impulses, but they were more sensitive to crack with bigger loads. Kujala and Klanac (2005) have also listed the main benefits of laser welded corrugated panels. These panels have shown, for example, good mechanical properties, such as thermal resistance, good vibration absorption, increased stiffness, and good blast loading resistance (Karlsson & Å ström 1997; Liang et al. 2001; Kujala & Klanac 2005; Tian & Lu 2005; Zhang et al. 2015). The fatigue strength of the laser-welded lap joints have been studied widely and the behavior is well-understood for different materials. For example, Cho et al. (2004) used finite element analysis to estimate fatigue strength for laser-welded lap joint successfully. Kamran et al. (2014) studied lap joints fatigue behavior of high strength low alloy steels. They noticed that the failure modes under quasi-static and cyclic loading are different. Under quasi-static loading condition, the crack will initiate from the base material and finally cracked through the lower sheet. Under low cycle loading, the crack will start growing from the preexisting crack tips and cracked through the lower sheet. When testing was made under high-cycle loading, the crack started to grow from preexisting crack tips and failed from the kinked fatigue crack through the upper sheet.

Numerical Analysis of Steel I-Core Sandwich Panels Subjected to Multiple Consecutive Blast Scenarios

The nonlinear dynamic response of steel I-core sandwich panels under three multiple consecutive blast scenarios using five different explosive charges has been numerically investigated. The obtained results are compared with available experimental data to verify the developed finite element model, and good agreement is observed. Special emphasis is placed on the evaluation of maximum displacements of cover plates and energy dissipation of different parts of the panels. According to the results, sandwich panels show better performance than equivalent solid plate with the same mass and material when subjected to consecutive blasts. Overall responses of panels are dependent on not only blast pressure, but also the sequence of loading. In this regard, three different phases of deformation based on blast pressure and sequence are observed in the response of panels when subjected to multiple blasts.

Response of square honeycomb core sandwich panels to granular matter impact

The deformation of square honeycomb core, stainless steel sandwich panels by the impact of explosively accelerated granular matter has been investigated and compared to results from a previous study using equivalent (same material and mass per unit area) solid plates subjected to similar impulsive loadings. Spherical explosive charges surrounded by 25–150 kg mass annular shells of water-saturated granular media (either fused silica or zirconia particles) were suspended above the center of the edge clamped test panels. The radially expanding granular particle front velocities were measured from high-speed video images, and revealed that the granular matter had been accelerated to velocities of 500–1200 m/s after detonation. A Kolsky bar was used to measure the time-dependent pressure and impulse at a position equivalent to the panel center, while the permanent deflections of the sandwich panels were determined by profilometry after the experiments. Even though fracture of electron beam welds used to attach the back face sheet to the sandwich panel core occurred in all the tests, the permanent deflections of the sandwich panel back faces were significantly less than those of equivalent solid plates, and were accompanied by minimal core compression. Discrete particle simulations of the granular matter acceleration and impact loading of the sandwich panels indicated that their superior deflection benefit arose from their high bending resistance rather than particle-structure interactions. This benefit was offset when the rear face of the sandwich was kept the same distance from the impulsive source as that of the solid plate since the impact face of the sandwich panel was closer to the impulsive source, subjecting it to a higher impulse than the solid plate. However, a substantial deflection reduction was still achieved by use of a strong core sandwich design.

Numerical investigation of the response of I-core sandwich panels subjected to combined blast and fragment loading

The LS-DYNA software was employed to investigate the dynamic response of I-core sandwich panels under combined blast and fragment loading. The combined blast loading was simulated by placing pre-fabricated fragments at the bottom surface of bare explosive. To facilitate evaluating the synergistic effect under combined blast loading, the resistance of sandwich panels under bare blast loading was also assessed. The results demonstrated that the damage caused by combined blast loading was more severe than that by bare blast loading. The roles of charge mass, face-sheet configuration and core configuration on the deformation/failure behavior and energy absorption characteristics of panels were analyzed and discussed in detail. Under combined blast loading, the panels exhibited a perforation and tearing failure mode accompanied by structural fragments from failed front face. The charge mass is relevant to whether the residual momentum of fragments is large enough to penetrate the back face. The face-sheet configuration that had thick front face and thin back face was favorable in mitigating the damage response. The core configuration with dense core webs provided more assistance in preventing the appearance of failure pattern with a large connected region. The face-sheet configuration and core configuration have negligible influence on the total energy absorption, but they would redistribute the energy dissipation among each panel component. Furthermore, the comparisons of blast resistance between sandwich panels and conventional monolithic counterparts were made. It turned out that the sandwich panels experienced lower level damage failure on back face but dissipated similar energy relative to equivalent solid plates.

Proposed formulas for evaluation of the equivalent material properties of a multiholed structure

It is widely known that the development of fine mesh in the immediate vicinity of the holes in a multiholed plate is a challenging issue. In practice, due to the amount of time consumed and the quality of the modelling, it is not desirable to model the structural characteristics of a multiholed plate in detail. In this regard, an effective means by which to avoid the unnecessary work of simulating a multiholed plate is to replace it with an equivalent solid plate while considering the decrease in stiffness associated with the increasing area of the holes. The objective of this study is to numerically and experimentally investigate the equivalent material properties of a multiholed plate of stainless steel 316L with respect to ligament efficiencies. Simple design formulas are proposed to determine the equivalent material properties of a multiholed plate that is completely perforated with closely spaced circular holes in a square or diagonal pattern by means of nonlinear finite-element method computations. It is concluded that the proposed formulas are accurate for prediction of the equivalent material properties of multiholed structures for their design and engineering.

Numerical and experimental investigation on broadband wave propagation features in perforated plates

Perforated plates are widely used in various engineering applications. Their mechanical and dynamical behaviours need to be investigated for the design and optimization purpose. In this work, the wave propagation features on broadband in perforated plates are predicted by a Condensed Wave Finite Element Method (CWFEM). Based on the wave dispersion relation identified by CWFEM, wave-based homogenization methods are proposed to define equivalent solid plates. Three perforated plates with different penetration patterns and hole shapes are considered and the accuracy of the equivalent homogenized model is illustrated by comparing it with finite element method. Experimental validation of the computed wave propagation characteristics on the two models is provided as well. A good correlation is observed not only at low frequency where homogenized model can be found, but also at mid and high frequency, where the wave beaming effect phenomenon occurs.

Non-linear Dynamic Analysis of Steel Hollow I-core Sandwich Panel under Air Blast Loading

In this paper, the non-linear dynamic response of novel steel sandwich panel with hollow I-core subjected to blast loading was studied. Special emphasis is placed on the evaluation of midpoint displacements and energy dissipation of the models. Several parameters such as boundary conditions, strain rate, mesh dependency and asymmetrical loading are considered in this study. The material and geometric non-linearities are also considered in the numerical simulation. The results obtained are compared with available experimental data to verify the developed FE model. Modeling techniques are described in detail. According to the results, sandwich panels with hollow I-core allowed more plastic deformation and energy dissipation and less midpoint displacement than conventional I-core sandwich panels and also equivalent solid plate with the same weight and material.

Experimental and numerical investigations on laser-welded corrugated-core sandwich panels subjected to air blast loading

Experimental investigations on the laser-welded triangular corrugated core sandwich panels and equivalent solid plates subjected to air blast loading are presented. The experiments were conducted in an explosion tank considering three levels of blast loading. Results show that the maximum deflection, core web buckling and core compaction increased as the decrease of stand-off distance. Back face deflections of sandwich panels were found to be nearly half that of equivalent solid plates at the stand-off distances of 100 mm and 150 mm. At the closest stand-off distance of 50 mm, the panel was found to fracture and fail catastrophically. Autodyn-based numerical simulations were conducted to investigate the dynamic response of sandwich panels. A good agreement was observed between the numerical calculations and experimental results. The model captured most of the deformation/failure modes of panels. Finally, the effects of face sheet thickness and core web thickness on the dynamic response of sandwich panel were discussed.

Numerical Analysis of Dynamic Response of Corrugated Core Sandwich Panels Subjected to Near-Field Air Blast Loading

Three-dimensional fully coupled simulation is conducted to analyze the dynamic response of sandwich panels comprising equal thicknesses face sheets sandwiching a corrugated core when subjected to localized impulse created by the detonation of cylindrical explosive. A large number of computational cases have been calculated to comprehensively investigate the performance of sandwich panels under near-field air blast loading. Results show that the deformation/failure modes of panels depend strongly on stand-off distance. The beneficial FSI effect can be enhanced by decreasing the thickness of front face sheet. The core configuration has a negligible influence on the peak reflected pressure, but it has an effect on the deflection of a panel. It is found that the benefits of a sandwich panel over an equivalent weight solid plate to withstand near-field air blast loading are more evident at lower stand-off distance.

Impact response of aluminum corrugated core sandwich panels

The mechanisms of projectile penetration of extruded 6061T6 aluminum alloy sandwich panels with empty and alumina filled, triangular corrugated cores have been experimentally investigated using zero obliquity, 12.7 mm diameter hard steel projectiles whose diameter was about a half that of the core's unit cell width. We find that low momentum impacts are laterally deflected by interactions with the inclined webs of the empty core. Complete penetration occurred by shear-off within the impacted front face sheet, followed by stretching, bending and tensile fracture of the core webs and finally shear-off within the back face sheet. This combination of mechanisms was less effective at dissipating the projectiles kinetic energy than the shear-off (plugging) mechanism of penetration of the equivalent solid aluminum panel. Inserting ballistic grade alumina prisms in the triangular cross section spaces of the corrugated core significantly increased the panel's ballistic resistance compared to the empty panel. The presence of the hard ceramic led to severe plastic deformation and fragmentation of the projectile and comminution and macroscopic fracture of the ceramic. The Al/Al2O3 hybrid panel ballistic limit was reached when pairs of parallel cracks formed in the rear face sheet at core web-face sheet nodes. The separation distance between these cracks was dependent upon the location of the impact with respect to that of the web-face sheet nodes. Nodal impacts resulted in pairs of fractures that were separated by one cell width and a critical velocity below that of the equivalent solid plate. Impacts mid-way between pairs of nodes resulted in back face sheet crack pairs separated by twice the cell width, and a critical velocity higher than the equivalent solid plate. Using X-ray tomography we show this resulted from the formation of oval (not circular) cross section fracture conoids in the ceramics. The conoid angle was about 60° in the extrusion direction but only 30° in the transverse direction. This observation may have interesting consequences for a panel's resistance to a second, close proximity impact.

Wet-sand impulse loading of metallic plates and corrugated core sandwich panels

We have utilized a combination of experimental and modeling methods to investigate the mechanical response of edge-clamped sandwich panels subject to the impact of explosively driven wet sand. A porthole extrusion process followed by friction stir welding was utilized to fabricate 6061-T6 aluminum sandwich panels with corrugated cores. The panels were edge clamped and subjected to localized high intensity dynamic loading by the detonation of spherical explosive charges encased by a concentric shell of wet sand placed at different standoff distances. Monolithic plates of the same alloy and mass per unit area were also tested in an identical manner and found to suffer 15–20% larger permanent deflections. A decoupled wet sand loading model was developed and incorporated into a parallel finite-element simulation capability. The loading model was calibrated to one of the experiments. The model predictions for the remaining tests were found to be in close agreement with experimental observations for both sandwich panels and monolithic plates. The simulation tool was then utilized to explore sandwich panel designs with improved performance. It was found that the performance of the sandwich panel to wet sand blast loading can be varied by redistributing the mass among the core webs and the face sheets. Sandwich panel designs that suffer 30% smaller deflections than equivalent solid plates have been identified.

Transient cooling of electronic components by flat heat pipes

Abstract This paper presents a theoretical investigation of a Flat Heat Pipe (spreader) designed for the cooling of multiple electronic components in transient state. This model is a transient model, coupling 3D thermal model with a 2D hydrodynamic one through the mass flux of evaporation–condensation, which occurs in a mass conservation equation. The model makes it possible to obtain the FHP wall transient temperatures, the transient pressures, velocities and temperatures in both liquid and vapor phases. A comparison of the behaviour of the FHP and an equivalent solid plate submitted to a transient thermal cycle shows that the FHP enhanced the electronic components cooling for the long thermal cycle duration when the solid plate is more efficient for the very short transient thermal cycles. The FHP provides also a very low thermal resistance, which helps to minimise the temperature gradient and then the hot spots and overheating.

Finite-Element Modeling and Development of Equivalent Properties for FRP Bridge Panels

Fiber-reinforced polymer FRP composite materials are increasingly making their way into civil engineering applications. To reduce the self-weight and also achieve the necessary stiffness, sandwich panels are commonly used for FRP bridge decks. However, due to the geometric complexity of the FRP sandwich deck, convenient analysis and design methods for FRP bridge deck have not been developed. The present study aims at developing equivalent properties for a complicated sandwich panel configuration using finite- element modeling techniques. With equivalent properties, the hollowed sandwich panel can be transformed into an equivalent solid orthotropic plate, based on which deflection limits can be evaluated and designed. A procedure for the in-plane axial properties of the sandwich core has first been developed, followed by developing the out-of-plane panel properties for bending behavior of the panel. An application is made in the investigation of the stiffness contribution of wearing surface to the total stiffness of bridges with FRP panels. The wearing surface contribution is not usually accounted for in a typical design of bridges with traditional deck systems.

The resistance of metallic plates to localized impulse

The responses of metallic plates and sandwich panels to localized impulse are examined by using a dynamic plate test protocol supported by simulations. The fidelity of the simulation approach is assessed by comparing predictions of the deformations of a strong-honeycomb-core panel with measurements. The response is interpreted by comparing and contrasting the deformations with those experienced by the same sandwich panel (and an equivalent solid plate) subjected to a planar impulse. Comparisons based on the center point displacement reveal the following paradox. The honeycomb panel is superior to a solid plate when subjected to a planar impulse, but inferior when localized. The insights gained from an interpretation of these results are used to demonstrate that a new design with a doubly-corrugated soft core outperforms solid plates both for planar and localized impulses.

Hydroelastic response of a box-like floating fuel storage module modeled using non-conforming quadratic-serendipity Mindlin plate element

Presented herein are the hydroelastic responses of a floating fuel storage module under wave action. The box-like fuel storage module is modeled by an equivalent solid plate. For the analysis, a non-conforming quadratic-serendipity (NC-QS) element based on the Mindlin plate theory was developed. In this element, we make use of the reduced integration method and the superposition of non-conforming modes onto the basis function of the 8-node element in order to prevent spurious modes and shear locking phenomena. Thus the element may be applied for both thick and thin plates. The solution for the hydroelastic response involves solving the coupled plate–water equation and the water equation numerically using the hybrid finite element–boundary element (FE-BE) method. The coupled plate–water equation is derived by equating the force term in the Mindlin plate equation with the wave pressure distribution obtained from the linearized Bernoulli equation; whereas the boundary integral equation relates the displacement of the plate and water velocity potential using the free-surface Green’s function. Results of the displacement and water velocity potential are found to be more accurate when compared with existing solutions for special cases. Moreover, the stress resultants computed are significantly more accurate than previous results as spurious modes are eliminated.

Limit Load of Anisotropic Components Using the M-Beta Multiplier Method

The mβ-multiplier method is based on Mura’s extended variational theorems in plasticity, and has been applied previously to isotropic components containing notches and cracks. Lower bound limit loads rapidly converge to inelastic analysis results when the method is used in conjunction with elastic modulus adjustment procedures. In this paper, the mβ-multiplier method is applied to pressure components exhibiting anisotropy. Specifically, the method is applied to the limit load determination of a heat exchanger tubesheet, wherein the tubesheet is modeled as an equivalent solid plate with anisotropic properties. Results are presented for a finite element model where plasticity is represented with Hill’s yield criterion, and a model using a fourth order yield criterion that accounts for compressibility of the tubesheet.