In recent years advances in technology have allowed the transition of composite structures from secondary to primary structural components. Consequently, a lot of applications demand development of thicker composite structures to sustain heavier loads. Typical sandwich panels consist of two thin metallic or composite face sheets separated by a honeycomb or foam core. This configuration gives the sandwich panel high stiffness and strength and enables excellent energy absorption capabilities with little resultant weight penalty. This makes sandwich structures a preferred design for a lot of applications including aerospace, naval, wind turbines and civil industries. Most aerospace structures can be analyzed using shell and plate models and many such structures are modeled as composite sandwich plates and shells. Accurate theoretical formulations that minimize the CPU time without penalties on the quality of the results are thus of fundamental importance. The classical plate theory (CPT) and the first order shear deformation theory (FSDT) are the simplest equivalent single-layer models, and they adequately describe the kinematic behavior of most laminates where the difference between the stiffnesses of the respective phases is not huge. However, in the case of sandwich structures where the core is a much more compliant and softer material as compared to the face sheets the results from CPT and FSDT becomes highly inaccurate. Higher order theories in such cases can represent the kinematics better, may not require shear correction factors, and can yield much more accurate results. An advanced Extended Higher-order Sandwich Panel Theory (EHSAPT) which is a two-dimensional extension of the EHSAPT beam model that Phan presented is developed. Phan had extended the HSAPT theory for beams that allows for the transverse shear distribution in the core to acquire the proper distribution as the core stiffness increases as a result of non-negligible in-plane stresses. The HSAPT model is incapable of capturing the in-plane stresses and assumes negligible in-plane rigidity. The current research extends that concept and applies it to two-dimensional plate structures with variable aspect ratios. The theory assumes a transverse displacement in the core that varies as a second order equation in z and the in-plane displacements that are of third order in z, the transverse coordinate. This approach allows for five generalized coordinates in the core (the in-plane and transverse displacements and two rotations about the x and y-axes respectively). The major assumptions of the theory are as follows: 1) The face sheets satisfy the Euler-Bernoulli assumptions, and their thicknesses are small compared to the overall thickness of the sandwich section; they undergo small strains with moderate rotations. 2) The core is compressible in the transverse and axial directions; it has in-plane, transverse and shear rigidities. 3) The bonding between the face sheets and the core is assumed to be perfect. The kinematic model is developed by assuming a displacement field for the soft core and then enforcing continuity of the displacement field across the interface between the core and facesheets. The constitutive relations are then defined, and variational and energy techniques are employed to develop the governing equations and associated boundary conditions. A static loading case for a simply supported sandwich plate is first considered, and the results are compared to existing solutions from Elasticity theory, Classical Plate Theory (CPT) and First-Order Shear Deformation Plate Theory (FSDT). Subsequently, the governing equations for a dynamic analysis are developed for a laminated sandwich plate. A free vibration problem is analyzed for a simply supported laminated sandwich plate, and the results for the fundamental natural frequency are compared to benchmark elasticity solutions provided by Noor. After validation of the new Extended Higher Order Sandwich Panel Theory (EHSAPT), a parametric study is carried out to analyze the effect of variation of various geometric and material properties on the fundamental natural frequency of the structure. After the necessary verification and validation of the theory by comparing static and free vibration results to elasticity solutions, a nonlinear static analysis for square and rectangular plates is carried out under various sets of boundary conditions. The analysis was carried out using variational techniques, and the Ritz method was used to find an approximate solution. The kinematics were developed for a sandwich plate undergoing small strain and moderate rotations and nonlinear strain displacement relations were evaluated. Approximate and assumed solutions satisfying the geometric boundary conditions were developed and substituted in the total potential energy relations. After carrying out the spatial integrations, the total potential energy was then minimized with respect to the unknown coefficients in the assumed solution resulting in nonlinear simultaneous algebraic equations for the unknown coefficients. The simultaneous nonlinear equations were then solved using the Newton-Raphson method. A convergence study was carried out to study the effect of varying the number of terms in the approximate solution on the overall result and rapid convergence was observed. The rapid convergence can be attributed to the fact that the assumed approximate solution not only satisfies the geometric boundary conditions of the problem but also the natural boundary conditions. During calculations four cases of boundary conditions were considered 1) Simply Supported with moveable edges. 2) Simply Supported with fixed edges. 3) Clamped with moveable edges. 4) Clamped with fixed edges. For movable boundary conditions, in-plane displacements along the normal direction to the supported edges are allowed whereas the out-of-plane displacement is fixed. For the immovable boundary condition cases, the plate is prevented from both in-plane and out-of-plane displacements along the edges. For the simply supported cases rotations about the tangential direction are allowed, and for the clamped cases no rotations are allowed.In recent years advances in technology have allowed the transition of composite structures from secondary to primary structural components. Consequently, a lot of applications demand development of thicker composite structures to sustain heavier loads. Typical sandwich panels consist of two thin metallic or composite face sheets separated by a honeycomb or foam core. This configuration gives the sandwich panel high stiffness and strength and enables excellent energy absorption capabilities with little resultant weight penalty. This makes sandwich structures a preferred design for a lot of applications including aerospace, naval, wind turbines and civil industries. Most aerospace structures can be analyzed using shell and plate models and many such structures are modeled as composite sandwich plates and shells. Accurate theoretical formulations that minimize the CPU time without penalties on the quality of the results are thus of fundamental importance. The classical plate theory (CPT) and the first order shear deformation theory (FSDT) are the simplest equivalent single-layer models, and they adequately describe the kinematic behavior of most laminates where the difference between the stiffnesses of the respective phases is not huge. However, in the case of sandwich structures where the core is a much more compliant and softer material as compared to the face sheets the results from CPT and FSDT becomes highly inaccurate. Higher order theories in such cases can represent the kinematics better, may not require shear correction factors, and can yield much more accurate results. An advanced Extended Higher-order Sandwich Panel Theory (EHSAPT) which is a two-dimensional extension of the EHSAPT beam model that Phan presented is developed. Phan had extended the HSAPT theory for beams that allows for the transverse shear distribution in the core to acquire the proper distribution as the core stiffness increases as a result of non-negligible in-plane stresses. The HSAPT model is incapable of capturing the in-plane stresses and assumes negligible in-plane rigidity. The current research extends that concept and applies it to two-dimensional plate structures with variable aspect ratios. The theory assumes a transverse displacement in the core that varies as a second order equation in z and the in-plane displacements that are of third order in z, the transverse coordinate. This approach allows for five generalized coordinates in the core (the in-plane and transverse displacements and two rotations about the x and y-axes respectively). The major assumptions of the theory are as follows: 1) The face sheets satisfy the Euler-Bernoulli assumptions, and their thicknesses are small compared to the overall thickness of the sandwich section; they undergo small strains with moderate rotations. 2) The core is compressible in the transverse and axial directions; it has in-plane, transverse and shear rigidities. 3) The bonding between the face sheets and the core is assumed to be perfect. The kinematic model is developed by assuming a displacement field for the soft core and then enforcing continuity of the displacement field across the interface between the core and facesheets. The constitutive relations are then defined, and variational and energy techniques are employed to develop the governing equations and associated boundary conditions. A static loading case for a simply supported sandwich plate is first considered, and the results are compared to existing solutions from Elasticity theory, Classical Plate Theory (CPT) and First-Order Shear Deformation Plate Theory (FSDT). Subsequently, the governing equations for a dynamic analysis are developed for a laminated sandwich plate. A free vibration problem is analyzed for a simply supported laminated sandwich plate, and the results for the fundamental natural frequency are compared to benchmark elasticity solutions provided by Noor. After validation of the new Extended Higher Order Sandwich Panel Theory (EHSAPT), a parametric study is carried out to analyze the effect of variation of various geometric and material properties on the fundamental natural frequency of the structure. After the necessary verification and validation of the theory by comparing static and free vibration results to elasticity solutions, a nonlinear static analysis for square and rectangular plates is carried out under various sets of boundary conditions. The analysis was carried out using variational techniques, and the Ritz method was used to find an approximate solution. The kinematics were developed for a sandwich plate undergoing small strain and moderate rotations and nonlinear strain displacement relations were evaluated. Approximate and assumed solutions satisfying the geometric boundary conditions were developed and substituted in the total potential energy relations. After carrying out the spatial integrations, the total potential energy was then minimized with respect to the unknown coefficients in the assumed solution resulting in nonlinear simultaneous algebraic equations for the unknown coefficients. The simultaneous nonlinear equations were then solved using the Newton-Raphson method. A convergence study was carried out to study the effect of varying the number of terms in the approximate solution on the overall result and rapid convergence was observed. The rapid convergence can be attributed to the fact that the assumed approximate solution not only satisfies the geometric boundary conditions of the problem but also the natural boundary conditions. During calculations four cases of boundary conditions were considered 1) Simply Supported with moveable edges. 2) Simply Supported with fixed edges. 3) Clamped with moveable edges. 4) Clamped with fixed edges. For movable boundary conditions, in-plane displacements along the normal direction to the supported edges are allowed whereas the out-of-plane displacement is fixed. For the immovable boundary condition cases, the plate is prevented from both in-plane and out-of-plane displacements along the edges. For the simply supported cases rotations about the tangential direction are allowed, and for the clamped cases no rotations are allowed.

No description available.

Much of the work done on active and passive constrained layer beams is done with mathematical models proposed by Kerwin and extended by DiTaranto, Mead and Markus, and others. The mathematics proposed by these early researchers was tailored to fit the damping treatments in use at that time: thin foil damping tapes applied to panels for noise reduction. A key assumption was that all layers had identical transverse displacements. While these assumptions are reasonable when the core layer, normally a soft viscoelastic material(VEM), is thin and the constraining layer is weak in bending, there are many situations in industry and in the literature where the ``Mead and Markus'' (MM) assumptions should be questioned. An important consequence of the MM modeling assumptions is that the strain energy in the VEM core is dominated by shear strain, and this in turn means that only the shear modulus is of primary importance. This is fortunate since only the shear modulus is available to engineers for viscoelastic materials used for layered damping treatments. It is a common practice in industry and academia to simply make an educated guess of the value of Poisson's ratio. It is shown in the dissertation that this can result in erroneous predictions of damping, particularly in partial-coverage configurations. Finite element analysis is used to model both the MM assumptions and a less-restrictive approach commonly used in industry. Predictions of damping from these models are compared against models with elements from C0 elements and a C1-capable element that matches tractions at material interfaces. It is shown that the time-honored modal strain energy method is a good indicator of modeling accuracy. To assess the effects of the MM assumptions on an active PZT used as a constraining layer, closed-loop damping versus gain is determined using both the MM and higher order elements. For these analyses, the time-dependent properties of the viscoelastic material are represented by a Maxwell model using internal variables. Finally, the basic MM premise that all layers share the same transverse displacement is disproved by experiment. / Ph. D.

A reliability-based optimization (RBO) methodology was developed and applied to fiber-reinforced polymer (FRP) bridge decks. Commercially available software was used to optimize a FRP bridge deck panel by weight with structural reliability, stress, and deflection constraints. A methodology using optimization software, finite element analysis, and probabilistic analysis software was developed to examine the effects of load and resistance uncertainties in FRP bridge deck optimization. Eight modular deck designs were considered for use in the RBO methodology. Investigations into random variable sensitivities, design variable sensitivities, wheel positions, and buckling were conducted to minimize computational effort. Five models were eventually optimized with deterministic methods and the RBO methodology. Ply thicknesses were treated as design variables. Material parameters, design variables, and load were taken as random variables in the reliability calculations. A comparison of RBO designs was made with the best candidate chosen based on deck panel weight.

No description available.

published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

Dissertation (Ph.D.)--Auburn University, 2007. / Abstract. Vita. Includes bibliographic references.

Bi-layered materials are a reduced weight derivative of the sandwich structure and are comprised of one thin skin face reinforced by a thick layer of low density material. Bi-layered materials are characterized by high flexural stiffness and are a viable alternative to conventional sandwich materials in applications where the functional requirements can be met without the second face sheet of the sandwich. For structural applications bi-layered materials are required to have oil canning and buckling resistance. This work addresses the buckling of shallow bi-layered arches using numerical and analytical approaches. A numerical, finite element model is developed to simulate the buckling phenomenon and the results were compared with known experimental data. An analytical model was developed using the energy method analysis and the buckling load was predicted from the minimum energy criterion. Comparison of the numerical and analytical results yielded fairly good agreement. An imperfection analysis conducted by means of the numerical model indicated that the load carrying capacity of bi-layered structures is reduced by up to 40% due to the presence of material and geometric imperfections. A parametric study conducted using the analytical model has been described to setup design guidelines for shallow bi-layered arches. It was found that the use of bi-layered structures can result in weight reduction of around 70% when compared with equivalent single layered structure.

Sandwich composites with polymer foam core are currently used in load-bearing components in buildings and naval structures due to their high strength to weight and stiffness to weight ratios, excellent thermal insulation, and ease of manufacturing. During their service time, sandwich composites are exposed to various external mechanical and hygro-thermal stimuli. It is known that the constituent properties of the sandwich composites are greatly influenced by the temperature and moisture fields. For example extreme temperature changes and humid environmental conditions can significantly degrade the stiffness and strength of the polymer foam core. This study analyzes the effect of moisture diffusion on the deformation of viscoelastic sandwich composites, which are composed of orthotropic fiber-reinforced laminated skins and viscoelastic polymeric foam core. It is assumed that the elastic and time-dependent (transient) moduli at any particular location in the foam core depend on the moisture concentration at that location. Sequentially coupled analyses of moisture diffusion and deformation are performed to predict overall performance of the studied viscoelastic sandwich systems. A time and moisture dependent constitutive model is used for the polymer foam core. A time-integration algorithm is developed to link this constitutive model to finite element (FE) analyses framework. The overall time-dependent responses of the sandwich composites subject to moisture diffusion are analyzed using 2D plane strain and 3D continuum elements. A 23% increase in the transverse deformation of the viscoelastic sandwich beam is observed due to the moisture degradation. Experimental data and analytical models available in the literature are used to verify the results obtained from the FE code. Parametric studies on the effects of different diffusivity ratios of skin and core materials on stress, strain and displacement fields have been analyzed. At the initial times the effect of moisture on the field variables is found to be most pronounced in the case with the highest diffusivity ratio. Contributions of moisture dependent elastic and the time-dependent moduli to the overall stress, strain and displacement field have been studied. The structural analysis of the sandwich composite under combined moisture diffusion and mechanical loading for two kinds of problems using FE method is performed to complete the study.

Bi-layered materials are a reduced weight derivative of the sandwich structure and are comprised of one thin skin face reinforced by a thick layer of low density material. Bi-layered materials are characterized by high flexural stiffness and are a viable alternative to conventional sandwich materials in applications where the functional requirements can be met without the second face sheet of the sandwich. For structural applications bi-layered materials are required to have oil canning and buckling resistance. This work addresses the buckling of shallow bi-layered arches using numerical and analytical approaches. A numerical, finite element model is developed to simulate the buckling phenomenon and the results were compared with known experimental data. An analytical model was developed using the energy method analysis and the buckling load was predicted from the minimum energy criterion. Comparison of the numerical and analytical results yielded fairly good agreement. An imperfection analysis conducted by means of the numerical model indicated that the load carrying capacity of bi-layered structures is reduced by up to 40% due to the presence of material and geometric imperfections. A parametric study conducted using the analytical model has been described to setup design guidelines for shallow bi-layered arches. It was found that the use of bi-layered structures can result in weight reduction of around 70% when compared with equivalent single layered structure.