Recent Advances in Sensitivity Analysis for Nonlinear Structural Mechanics Problems

Previous studies on the thermal buckling of sandwich plates with composite face sheets indicate that only thin skins with high stiffness and low coefficients of thermal expansion (CTE) can lead to the desired buckling temperatures. Thus, carbon nanotubes (CNTs) that can significantly enhance thermo-mechanical properties of fibre-reinforced polymer composites are used in the present study to increase the critical buckling temperature of sandwich plates with soft core and laminated composite face sheets. First, a comprehensive series of experimental tests are conducted to evaluate the effects of nanotubes on thermo-mechanical properties of the face sheets. The experimental results indicate that using only 0.3% CNTs considerably increases the longitudinal and transverse Young’s modulus and shear modulus of the carbon fibre/epoxy composite face sheets. The obtained data also show that CNTs significantly decrease the CTE of composite skins. Subsequently, thermal buckling equations of sandwich plates with CNT-reinforced composite face sheets are derived based on piecewise low-order shear deformation theory (PLSDT). Three analytical, semi analytical, and numerical methods are used to investigate thermal buckling behaviour of the sandwich plates with various boundary conditions. To verify the results, several comparisons are performed, which show that the implemented methods can predict the buckling temperatures of sandwich plates with high accuracy. Finally, a parametric study is conducted to examine the effects of CNTs on the thermal buckling of sandwich plates for different length to thickness ratios, thicknesses of face sheets, stacking sequences of layers, and various types of boundary conditions. The results indicate that CNTs can increase the critical buckling temperature of sandwich plates by 22%–36%, based on the layup, geometrical parameters, and boundary conditions.

Large amplitude free vibration of sandwich beams with flexible core and FG Graphene Platelet Reinforced Composite (FG-GPLRC) face sheets based on extended higher-order sandwich panel theory

This paper discusses implementation and adaptivity of the Discontinuous Galerkin (DG) finite element method as applied to linear and non-linear structural dynamic problems. By the DG method, both displacements and velocities are approximated as piecewise bilinear functions in space and time and may be discontinuous at the discrete time levels. Both implicit and explicit iterative algorithms for solving the resulted system of coupled equations are derived. They are third-order accurate and, while the implicit procedure is unconditionally stable, the explicit one is conditionally stable. An h-adaptive procedure based on the Zienkiewicz–Zhu error estimate using the SPR technique is applied. Numerical examples are presented to show the suitability of the DG method for both linear and non-linear structural dynamic analysis. Copyright © 1999 John Wiley & Sons, Ltd.

In this study, Bi-Grid, Tri-Grid, Quadri-Grid and Kagome-Grid honeycombs were designed and fabricated using 3D printing technology Sandwich composites were prepared by gluing the cores and composite face sheets together. Mechanical performance of the sandwich structures were characterized using finite element analysis and three-point bending test. Results indicate that when suffering from bending loads, the stress concentrations are located at the loading zone on upper face sheets (distributed in both sides of the indenter) and supporting zone on bottom face sheets, and the stress concentration zones of the honeycomb cores are located in the area that between indenter and supports. The failure mechanism of the Bi-Grid sandwich structure is interfacial de-bonding between composite face sheet and Bi-Grid core, and the failure modes of the Tri-Grid, Quadri-Grid and Kagome-Grid are core shear. The mechanical performance of Quadri-Grid sandwich structure is better than that of the other three structures.

The parallel implicit time‐integration algorithm (PITA) is among a very limited number of time‐integrators that have been successfully applied to the time‐parallel solution of linear second‐order hyperbolic problems such as those encountered in structural dynamics. Time‐parallelism can be of paramount importance to fast computations, for example, when space‐parallelism is unfeasible as in problems with a relatively small number of degrees of freedom in general, and reduced‐order model applications in particular, or when reaching the fastest possible CPU time is desired and requires the exploitation of both space‐ and time‐parallelisms. This paper extends the previously developed PITA to the non‐linear case. It also demonstrates its application to the reduction of the time‐to‐solution on a Linux cluster of sample non‐linear structural dynamics problems. Copyright © 2008 John Wiley & Sons, Ltd.

In this study, we experimentally investigate the impact damage and failure mechanisms of foam-core sandwich composites with carbon fiber reinforced polymer (CFRP) and/or glass fiber reinforced polymer (GFRP) face sheets. Specimens are conditioned and impacted over a wide temperature range (from room temperature of 23°C down to -70°C) using Instron CEAST 9350 impact test machine. This work also explores the use of hybrid composite face sheets, with various configurations of layering CFRP and GFRP in the face sheets of foam-core sandwich composites. Results show that exposure to low temperature causes more severe damage, particularly in specimens with CFRP face sheets, due to their extreme brittleness. GFRP face sheet specimens are able to achieve larger deformation and absorb greater impact energy even at low temperature conditions. There is a significant benefit in using hybrid configurations, by striking a balance between brittle (CFRP) and ductile (GFRP) materials and harnessing their mechanical advantages of high strength and high fracture toughness, respectively. Results also demonstrate that hybridization is a solution to reduce temperature effects in impact deformation. Careful placement of CFRP and GFRP in layup order can harness the best impact performance. X-ray micro-computed tomography (μCT) images reveal substantial delamination at the interfaces between CFRP and GFRP layers. It is also observed that CFRP layers fail by brittle fracture, while delamination is the major damage mode within GFRP layers. Other complex failure mechanisms in the composite face sheets (such as matrix crack and fiber breakage) and foam core (core crushing, core shearing and interfacial debonding) are also presented.

A new super convergent sandwich beam finite element formulation is presented in this article. This element is a two-nodded, six degrees of freedom (dof) per node (3 dof u0, w, φ for top and bottom face sheets each), which assumes that all the axial and flexural loads are taken by face sheets, while the core takes only the shear loads. The beam element is formulated based on first-order shear deformation theory for the face sheets and the core displacements are assumed to vary linearly across the thickness. A number of numerical experiments involving static, free vibration, and wave propagation analysis examples are solved with an aim to show the super convergent property of the formulated element. The examples presented in this article consider both metallic and composite face sheets. The formulated element is verified in most cases with the results available in the published literature.

An analytical solution for vibro-acoustic characteristics of sandwich panel with 3DGrF core and FG-CNT reinforced polymer composite face sheets

The amount of impact energy used to damage a composite laminate face sheet of a sandwich structure is a critical parameter when assessing residual compression strength. The compression after impact strength of impacted laminates used as face sheets on honeycomb core sandwich structure is dependent upon how thick the face sheet laminate is and this has traditionally been accounted for by normalizing (dividing) the impact energy by the laminate’s thickness. However when comparing compression after impact strength values for a given lay-up sequence and fiber/resin system, dividing the impact energy by the specimen thickness has been noted by the author to give higher compression after impact strength values for thicker face sheet laminates. A study was thus undertaken to assess the comparability of compression after impact strength data of sandwich structure by normalizing the impact energy by the face sheet thickness raised to a power to account for the higher strength of thicker laminates. Two data sets generated in this study were analyzed by dividing the impact energy by the face sheet thickness to the 1.0, 1.5, 2.0 and 2.5 powers. Results show that raising the face sheet thickness to a power of approximately 2.5 and dividing the impact energy by this quantity yields more comparable compression after impact strength data for comparing 8- and 16-ply face sheet laminates. For comparison of 24-ply face sheet laminates to 8- or 16-ply face sheet laminates, a value closer to 2 was found to give more comparable compression after impact strength data.

Nonlinear structural analysis, which can account for geometrical or material nonlinearities beyond the scope of linear methods, typically incurs high computational costs. Recent advances have shown that quantum computers can accelerate various numerical simulations. Although quantum acceleration of linear structural analysis via the Quantum Linear System Algorithm (QLSA) has been studied, its application to nonlinear structural analysis remains unexplored. Here, we introduce our proposed quantum algorithm for accelerating nonlinear structural analysis, summarizing its key features and performance results from our recent study.

A method of measuring the mode I (peeling) fracture toughness of core/face sheet bonds in sandwich structures is desired, particularly with the widespread use of models that need this data as input. This study examined if a mode I critical strain energy release rate, GIC, can be obtained from the climbing drum peel (CDP) test. The CDP test is relatively simple to perform and does not rely on measuring small crack lengths such as required by the more commonly used double cantilever beam (DCB) test. Simple energy methods were used to calculate GIC from CDP test data on composite face sheets bonded to a honeycomb core. Face sheet thicknesses from 2 to 5 plies (0.51—1.27 mm) were tested to examine the upper and lower bounds on face sheet thickness requirements. Suggestions on conducting the test and on modifying the CDP apparatus to test composite face sheets (as opposed to metallic) are also presented. Results from the study suggest that the CDP test, with certain provisions, can be used to find the GIC value of a core/face sheet bond.

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.

Combining eddy current, thermography and laser scanning to characterize low-velocity impact damage in aerospace composite sandwich panels

Adjoint design sensitivity analysis and optimization of nonlinear structures using geometrical mapping approach

ABSTRACTTwo algorithms are proposed for direct time integration of an equation of motion of structural dynamics problems. The performance of the proposed methods is examined by evaluating stability, order of accuracy, numerical dissipation, and algorithmic damping. The results show that critical time for instability of the proposed algorithms is larger than those of conditionally stable methods. The numerical dissipation is shown to be explicitly less than other methods. Furthermore, the proposed algorithms are non-dissipative in the low-frequency range and have favorable damping in mid- and high-frequency regimes. Three examples are carried out to evaluate the feasibility and effectiveness of the proposed algorithms.