Planar Bending of Sandwich Beams with Transverse Loads off the Centroidal Axis

Conventional analysis methods for beams do not distinguish between transverse loads that are applied at the beam centroidal axis and those acting either above or below the centroidal axis. In contrast, this paper formulates a sandwich beam finite element solution which models the effect of load height relative to the centroidal axis. Towards this goal, the governing equilibrium equations and associated boundary conditions are derived based on a Timoshenko beam formulation for the core material. Special shape functions satisfying the homogeneous form of the equilibrium equations are derived and subsequently used to formulate exact stiffness matrices. By omitting the stiffness terms related to the faces, the formulation for a homogeneous Timoshenko beam can be recovered. Also, the Euler–Bernouilli counterpart of the formulation is recovered as a limiting case of the current Timoshenko beam formulation. Effects of load height relative to the centroid are observed to have similarities with those induced by axial forces in beam-columns. For a simply supported beam, downward acting loads located below the centroidal axis are found to induce a stiffening effect while those acting above the centroidal axis are found to induce a softening effect, resulting in higher transverse displacements.     

Effects of Bonding Stiffness on Thermal Stresses in Sandwich Panels

Sandwich panels made of thin skins and a lightweight core expand and∕or bow when subjected to temperature changes. The significance of induced thermal stresses in the panels depends on material properties. The effects of bonding layers on these stresses were not investigated in available works on the structural analysis of sandwich panels. This paper presents elasticity solutions for thermal stresses in sandwich panels with interlayer slip. The effects of finite bonding stiffnesses on the structural behavior of the panels are investigated. The numerical results show that the bonding stiffness, up to a certain level, has a strong effect on panel structural response. The answer to what constitutes perfect bonding is best answered in terms of the ratio of the core stiffness to the bonding stiffness. A heat chamber is designed and used to test sandwich specimens under different temperature changes. The experimental values for normal stresses in the skins are in good agreement with the present theory.     

Response of Curved Sandwich Panels Subjected to Blast Loading

Curved sandwich panels with two aluminium face sheets and an aluminium foam core under air blast loadings were investigated experimentally and numerically. Specimens with two values of radius of curvature and different core/face sheet configurations with the same projected area were tested for three blast intensities. All four edges of the panels were fully clamped. The experiments were carried out by a four-cable ballistic pendulum with corresponding sensors. The impulse acting on the front face of the assembly, the deflection history at the center of the back face sheet, and the strain history at some characteristic points on the back face were obtained. Then the deformation/failure modes of specimens were classified and analyzed systematically. The commercial software LS-DYNA was employed to simulate those physical processes. The finite-element (FE) model was validated by the data from experiments. Detailed deformation and energy dissipation mechanisms were further revealed by the FE models. The valuable experimental data and results from FE models show that the initial curvature of a curved sandwich panel changes the deformation/collapse mode with an extended range for bending-dominated deformation mode, which suggests that the performance of the sandwich shell structures slightly exceeds that of both their equivalent solid counterpart and a flat sandwich plate in certain blast intensity ranges.     

Wrinkling and Edge Buckling in Orthotropic Sandwich Beams

A sandwich beam buckling problem is studied here using two-dimensional elasticity to model the beam constituents. The global and local instability of such a beam with orthotropic constituents under various boundary conditions are investigated. The face sheet and the core are assumed to be linear elastic orthotropic continua. General buckling deformation modes of the sandwich beam subjected to uniaxial compressive loading are considered. The appropriate incremental stress and conjugate incremental finite-strain measure for the instability problem of the sandwich beam, and the corresponding constitutive model are addressed. It is shown that a sandwich beam having a core with a negligible stiffness compared to the face sheets is prone to fail by edge buckling. The present analysis is compared with several previous analytical studies and corresponding experimental results. Finite-element analyses are carried out for comparison against the theoretical predictions. The formulation used in the finite-element code is discussed in relation to the formulation adopted in the theoretical derivation.     

Structural Performance of Hybrid GFRP/Steel Concrete Sandwich Panels

Precast/prestressed concrete sandwich panels consist of two concrete wythes separated by a rigid insulation foam layer and are generally used as walls or slabs in thermal insulation applications. Commonly used connectors between the two wythes, such as steel trusses or concrete stems, penetrate the insulation layer causing a thermal bridge effect, which reduces thermal efficiency. Glass fiber-reinforced polymer (GFRP) composite shell connectors between the two concrete wythes are used in this research as horizontal shear transfer reinforcement. The design criterion is to establish composite action, in which both wythes resist flexural loads as one unit, while maintaining insulation across the two concrete wythes of the panel. The experiments carried out in this research show that hybrid GFRP/steel reinforced sandwich panels can withstand out-of-plane loads while providing resistance to horizontal shear between the two concrete wythes. An analytical method is developed for modeling the horizontal shear transfer enhancement using a shear flow approach. In addition, a truss model is built, which predicts the panel deflections observed in the experiments with reasonable accuracy.     

Steel Hexagonal Honeycomb Core Equivalent Elastic Moduli for Bridge Deck Sandwich Panels

Glass fiber-reinforced polymer (GFRP) materials possess inherently high strength-to-weight ratios, but their effective elastic moduli are low relative to civil engineering (CE) construction materials. While elastic modulus may be comparable to that of some CE materials, the lower shear modulus adversely affects stiffness. As a result, serviceability issues are what govern GFRP deck design in the CE bridge industry. An innovative solution to increase the stiffness of a commercial GFRP reinforced-sinusoidal honeycomb sandwich panel was proposed; this solution would completely replace the GFRP honeycomb core with a hexagonal honeycomb core constructed from commercial steel roof decking. The purpose of this study was to perform small-scale tests to characterize the steel hexagonal honeycomb core equivalent elastic moduli in an effort to simplify the modeling of the core. The steel core equivalent moduli experimental results were compared with theoretical hexagonal honeycomb elastic modulus equations from the literature, demonstrating the applicability of the theoretical equations to the steel honeycomb core. Core equivalent elastic modulus equations were then proposed to model and characterize the steel hexagonal honeycomb as applicable to sandwich panel design. The equivalent honeycomb core will enable an efficient sandwich panel stiffness design technique, both for structural analysis methods (i.e., hand calculations) and finite-element analysis procedures.     

Minimum Weight of a Sandwich Panel

The least‐weight problem of a sandwich panel with a truncated, hollow, hexagonal core, and subjected to a given bending moment along each edge is analyzed in this paper. In order to meet the practical manufacturing requirements and be within allowable stress limits, constraints are placed on the geometrical dimensions of the structural parts of the sandwich panel as well as on the physical strength, such as the allowable stresses. Upper and lower limiting values are assigned for each of the design variables. Through the use of the penalty function, the minimization problem subjected to a set of twenty inequality constraints is changed to a sequence of unconstrained ones. The modified Fletcher‐Powell method is used by a proper choice of the penalty parameter and the reduction factor. The methodology presented here can be extended to include multiple loading conditions, bending rigidity, and shear rigidity requirements, which present no additional difficulties except to increase the number of constraints.     

Evaluation of GFRP Honeycomb Beams for the O’Fallon Park Bridge

This paper presents a study on the evaluation of the static performance of a glass fiber-reinforced polymer (GFRP) bridge deck that was installed in O’Fallon Park over Bear Creek west of the City of Denver. The bridge deck has a sandwich panel configuration, consisting of two stiff faces separated by a light-weight honeycomb core. The deck was manufactured using a hand lay-up technique. To assist the preliminary design of the deck, the stiffness and load-carrying capacities of four approximately 330 mm (13 in.) wide GFRP beam specimens were evaluated. The crushing capacity of the panel was also examined by subjecting four 330×305×190?mm?(13×12×7.5?in.) specimens to compression tests. The experimental data were analyzed and compared to results obtained from analytical and finite element models, which have been used to enhance the understanding of the experimental observations. The failure of all four beams was caused by the delamination of the top faces. In spite of the scatter of the tests results, the beams showed good shear strengths at the face-to-core interface as compared to similar panels evaluated in prior studies.     

Global and Local Buckling of a Sandwich Beam

A two-dimensional mechanical model is developed to predict the global and local buckling of a sandwich beam, using classical elasticity. The face sheet and the core are assumed as linear elastic isotropic continua in a state of planar deformation. The core is assumed to have two deformation modes: antisymmetrical and symmetrical with respect to the core geometric midplane. Characteristics of the two deformation modes and the corresponding buckling behavior are shown and it appears that they are identical when the buckling wavelength is short. The present analysis is compared with various previous analytical studies and corresponding experimental results. On the basis of the model developed here, validation and accuracy of several previous theories are discussed for different geometric and material properties of a sandwich beam. The results presented in this paper, verified through finite-element analysis and experiment, are an accurate prediction of the overall buckling behavior of a sandwich beam, for a wide range of material and geometric parameters.     

Natural Vibrations of Laminated and Sandwich Plates

An exact analytical solution based on the propagator matrix method and a semianalytical solution based on a higher-order mixed approach (displacement and stress interpolation) have been presented in this paper to evaluate the natural frequencies as well as the stress and displacement mode shapes of simply supported, cross-ply laminated and sandwich plates. Continuity of the transverse stresses and displacements has been maintained at the laminae interfaces. Results have been presented for orthotropic plates, symmetric as well as nonsymmetric cross-ply composite and sandwich laminates. Results from the propagator matrix agree well with the published results for frequencies as well as displacement and stress mode shapes. Furthermore, the frequencies and displacement and stress eigenvectors obtained from the proposed layerwise mixed method are in excellent agreement with those obtained by three-dimensional elasticity theory. Results obtained from the present equivalent single layer theory are in good agreement with those obtained from the displacement based higher order methods. The high accuracy of the present methods is further confirmed by comparing the response of a sandwich plate with significantly different layer properties for which the conventional displacement based formulations yield inaccurate solutions.     

Free-Vibration Analysis and Material Constants Identification of Laminated Composite Sandwich Plates

Free vibration of symmetrically laminated composite sandwich plates with elastic edge restraints is studied via the Rayleigh–Ritz approach. The proposed Rayleigh–Ritz method is constructed on the basis of the layer-wise linear displacement theory. The accuracy of the method in predicting natural frequencies of composite sandwich plates with different boundary conditions is verified by the results reported in the literature or the experimental data obtained in this study. The proposed method is then applied to the material constant identification of free composite sandwich plates using the first six theoretical natural frequencies of the plates. In the identification process, trial material constants are used in the present method to predict the theoretical natural frequencies, a frequency discrepancy function is established to measure the sum of the squared differences between the experimental and theoretical natural frequencies, and a stochastic global minimization algorithm is used to search for the best estimates of the material constants by making the frequency discrepancy function a global minimum. Applications of the material constant identification technique are demonstrated by means of several examples.     

Thermal Postbuckling Behavior of Composite Sandwich Plates

By considering the total transverse displacement of a sandwich plate as the sum of the displacement due to bending of the plate and that due to shear deformation of the core, a 72 degrees of freedom high precision high order triangular-plate element is developed for the thermal postbuckling analysis of rectangular composite sandwich plates. Due to an uneven thermal expansion coefficient in the two local material directions, the buckling mode of the plate can be changed from one mode to another as the fiber orientation or aspect ratio of the plate is varied. By examining the local minimum of total potential energy of each mode, a clear picture of buckle pattern change is presented. Numerical results show that for a sandwich plate with cross-ply laminated faces, buckle pattern change may occur when the plate has a long narrow shape. However, for sandwich plates with angle-ply laminated faces, the buckling mode is dependent on the fiber orientation and aspect ratio of the plate. The effect of temperature gradient on the postbuckling behavior of the sandwich plate is limited except for angle-ply laminated sandwich plates with fiber angle greater than 70° or less than 20°.     

Light-Weight Fiber-Reinforced Polymer Composite Deck Panels for Extreme Applications

Currently within the military there is a need for a universal light-weight bridge deck system capable of supporting extreme loads over a wide temperature range. This research presents the development, testing, and analysis of five different fiber-reinforced polymer (FRP) webbed core deck panels. The performance of the FRP webbed decks are compared with an existing aluminum deck and with a baseline balsa core system, which has previously been tested as part of the development of the composite army bridge for the US Army. The study shows that for one-way bending, the FRP webbed core can exceed the shear strength of the baseline balsa core by a factor of 3.2 at a core’s density, which is 28% lighter than the balsa baseline. In addition, weight savings in excess of 30% are shown for using FRP decking in place of conventional aluminum decking. Based on test results and finite-element analysis, the failure modes of the different FRP webbed cores are discussed and design recommendations for FRP webbed core decks are provided.     

Evaluation of Composite Sandwich Bridge Decks with Hybrid FRP-Steel Core

A hybrid concept of composite sandwich panel with hybrid fiber-reinforced polymer (FRP)—steel core was proposed for bridge decks in order to not only improve stiffness and buckling response but also be cost efficient compared to all glass fiber-reinforced polymer (GFRP) decks. The composite sandwich bridge deck system is comprised of wrapped hybrid core of GFRP grid and multiple steel box cells with upper and lower GFRP facings. Its structural performance under static loading was evaluated and compared with the ANSYS finite element predictions. It was found that the presented composite sandwich panel with hybrid FRP-steel core was very efficient for use in bridges. The thickness of the hybrid deck may be decreased by 19% when compared with the all GFRP deck. The failure mode of the proposed hybrid deck was more favorable because of the yielding of the steel tube when compared with that of all GFRP decks.     

Reinforcing Transverse Glulam Deck Panels with Through-bolted Glulam Stiffener Beams: Theoretical Analysis

Two design criteria, allowable stress design (ASD) and load and resistance factor design (LRFD), are presented for calculating glued-laminated (glulam) stiffener beam depth and number of dome head through bolts used in deck-to-deck connections for longitudinal stringer, transverse deck glulam bridges. Design examples for six deck panel spans (762–3,658 mm) and an applied 89 kN wheel load are also presented. The connection configurations (stiffener beam depth and number of dome head bolts) for both ASD and LRFD differ only in the stiffener beam depth (maximum 15% difference). Both ASD and LRFD criteria performed very well when compared to experimental observation and results of loaded stiffener beam connected deck panels.     

Lateral-Torsional Buckling of Stepped Beams with Continuous Bracing

Continuous span multibeam steel bridges are common along the state and interstate highways. The top flange of the beams is typically braced against lateral movement by the deck slab, and in many bridges the cross section is stepped at discrete points along the span. Design equations for lateral–torsional buckling (LTB) resistance in the American Association of State Highway and Transportation Officials “Load and resistance factor design bridge design specifications” are for prismatic beams and ignore the lateral restraint provided by the bridge deck. A new design equation is proposed that can be applied to I-shaped stepped beams with continuous top flange lateral bracing. By including the effects of the change in cross section size and the continuous top flange bracing, the calculated LTB resistance is significantly increased. Critical bending moment values from the proposed equation are compared to values from finite element method buckling analyses. The new equation is sufficiently accurate for use in design and in the evaluation of existing bridges.     

Vibration of Laminate-Faced Sandwich Plate by a New Refined Element

An efficient six-noded triangular element based on refined plate theory is developed for the analysis of sandwich plates with stiff laminated face sheets and it is applied to a free vibration problem in this paper. The plate theory represents parabolic through thickness variation of transverse shear stresses with continuity at the layer interfaces, which introduces discontinuity at these interfaces for the shear strains. It is to be noted that the plate theory requires unknowns at the reference plane only. Moreover, it ensures a shear stress-free condition at the top and bottom surfaces of the plate. Thus, the plate theory has all of the features required for an accurate modeling of laminated sandwich plates. The plate theory suffers from a problem in its finite element implementation since it requires C1 continuity of transverse displacement at the element interfaces. As very few elements based on this plate theory exist and they possess certain disadvantages, an attempt has been made to develop this new element. It has been utilized to study some interesting problems of laminated sandwich plate.     

Stability of Composite and Sandwich Struts by Mixed Formulation

A unified mixed, higher-order analytical formulation is presented to evaluate the buckling of laminated composite struts. The formulation can also be used to evaluate the overall buckling and wrinkling loads of a general multilayer, multicore sandwich strut having any arbitrary sequence of stiff layers and cores. The usual assumptions of thin stiff layers and antiplane core are advantageously eliminated. Displacements as well as transverse stress continuities are enforced in the formulation by incorporating them as the degrees of freedom, thus avoiding separate calculations of the modal transverse stresses. Two sets of mixed models are proposed, based on individual layer and equivalent single layer theories, by selectively incorporating nonlinear components of Green’s strain tensor. Limitations of the equivalent single-layer theories and typical simplifying assumptions are highlighted. A parametric investigation is presented, concerning the influence of the material and geometric properties on the buckling behavior of a sandwich strut. A few recommendations are also made for the stability analysis of laminated composite struts.     

Mechanics of Composite Sinusoidal Honeycomb Cores

Lightweight and heavy-duty fiber-reinforced polymer (FRP) composite honeycomb sandwich structures have been increasingly used in civil infrastructure. Unique cellular core configurations, such as sinusoidal core, have been applied in sandwich construction. Due to specific core geometry, the solutions for core effective stiffness properties are not readily available. This paper presents a mechanics of materials approach to evaluate the effective stiffness properties of sinusoidal cores. In particular, the internal forces of a curved wall in a unit cell are expressed in terms of resultant forces, and based on the energy method and principle of equivalence analysis, the in-plane stiffness properties of sinusoidal cores are derived. Both finite-element modeling and experimental testing are carried out to verify the accuracy of the proposed analytical formulation. To illustrate the present analytical approach as an efficient tool in optimal analysis and size selection of sinusoidal cores, several design plots are provided and discussed. The simplified analysis and formulation presented for sinusoidal cores can be used in design application of FRP honeycomb sandwich and optimization of efficient cellular core structures.     

Analysis of Laminated Sandwich Plates Based on Interlaminar Shear Stress Continuous Plate Theory

The bending response of sandwich plates with stiff laminated face sheets is studied by a six-noded triangular element having seven degrees of freedom at each node. The element formulation is based on a refined higher-order plate theory having all the features for an accurate modeling of sandwich plates with affordable unknowns. The refined plate theory is quite attractive but suffers from a problem concerned with an interelement continuity requirement when it is used in finite element analysis. The problem has been dealt satisfactorily in this new element, which is applied to the analysis of sandwich plates of different kinds.