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This study aims at improving the empirical correlation for estimating the yield strength from small punch tests. The currently used procedure in the European standard EN 10371 to determine the elastic-plastic transition force – based on bi-linear fitting – involves a dependency not only on the onset of plastic flow but also on the work hardening of the material. Consequently, the yield strength correlation factor is not universal but depends on the material properties and on the ge-ometry of the small punch set-up – leading to a significant uncertainty in the yield strength estima-tion. In this study, an alternative definition of the elastic-plastic transition force is proposed, which significantly less depends on the work hardening of the material and on the small punch geome-try. The approach is based on extensive elastic-plastic finite element simulations with generic ma-terial properties, including a systematic variation of the yield strength, ultimate tensile strength, and uniform elongation. The new definition of the transition force is based on the deviation of the force-deflection curve from the analytical elastic slope derived by Reissner's plate theory. A signifi-cant reduction of the uncertainty of the yield strength estimation is demonstrated.

Finite element simulations of the small punch test are performed.Generic elastic-plastic material properties are used. A systematic variation of the yield stress, ultimate tensile stress and uniform elongation is performed to investigate the effects of these parameters of the uniaxial stress-strain curve on the characteristics of small punch force-deflection curves. Moreover, the effect of sample thickness is studied. It is shown that the currently used elastic-plastic transition force – obtained by bi-linear fitting – does not only depend on the yield strength but also on the work hardening behavior of the material. An alternative definition of the elastic-plastic transition force is proposed, which significantly less depends on the work hardening of the material. The approach is based on the deviation of the force-deflection curve from the analytical elastic slope derived by Reissner's plate theory. The new definition of the transition force leads to significantly reduced dependence of the correlation factor on the geometry of the small punch set-up.

This thesis presents two studies on elastic plates. In the first study, we discuss the choice of elastic energies for thin plates and shells, an unsettled issue with consequences for much recent modeling of soft matter. Through consideration of simple deformations of a thin body in the plane, we demonstrate that four bulk isotropic quadratic elastic theories have fundamentally different predictions with regard to bending behavior. At finite thickness, these qualitative effects persist near the limit of mid-surface isometry, and not all theories predict an isometric ground state. We discuss how certain kinematic measures that arose in early studies of rod mechanics lead to coherent definitions of stretching and bending, and promote the adoption of these quantities in the development of a covariant theory based on stretches rather than metrics. In the second work, the effects of in-plane swelling gradients on thin, anisotropic plates are investigated. We study systems with a separation of scales between bending energy terms. Warped equilibrium shapes are described by two parameters controlling the spatial "rolling up'' and twisting of the surface. Shapes within this two-parameter space are explored, and it is shown that shapes will either be axisymmetric or twisted depending on swelling function parameters and material anisotropy. In some axisymmetric shapes, pitchfork bifurcations to twisted solutions are observed by varying these parameters. We also show that a familiar soft mode of the catenoid to helicoid transformation of an isotropic material no longer exists with material anisotropy.

This thesis presents two studies on elastic plates. In the first study, we discuss the choice of elastic energies for thin plates and shells, an unsettled issue with consequences for much recent modeling of soft matter. Through consideration of simple deformations of a thin body in the plane, we demonstrate that four bulk isotropic quadratic elastic theories have fundamentally different predictions with regard to bending behavior. At finite thickness, these qualitative effects persist near the limit of mid-surface isometry, and not all theories predict an isometric ground state. We discuss how certain kinematic measures that arose in early studies of rod mechanics lead to coherent definitions of stretching and bending, and promote the adoption of these quantities in the development of a covariant theory based on stretches rather than metrics. In the second work, the effects of in-plane swelling gradients on thin, anisotropic plates are investigated. We study systems with a separation of scales between bending energy terms. Warped equilibrium shapes are described by two parameters controlling the spatial "rolling up'' and twisting of the surface. Shapes within this two-parameter space are explored, and it is shown that shapes will either be axisymmetric or twisted depending on swelling function parameters and material anisotropy. In some axisymmetric shapes, pitchfork bifurcations to twisted solutions are observed by varying these parameters. We also show that a familiar soft mode of the catenoid to helicoid transformation of an isotropic material no longer exists with material anisotropy.

In structural analysis, many components are approximated as plates. More often that not, classical plate theories, such as Kirchhoff or Reissner-Mindlin plate theories, form the basis of the analytical developments. The advantage of these approaches is that they leads to simple kinematic descriptions of the problem: the plate's normal material line is assumed to remain straight and its displacement field is fully defined by three displacement and two rotation components. While such approach is capable of capturing the kinetic energy of the system accurately, it cannot represent the strain energy adequately. For instance, it is well known from three-dimensional elasticity theory that the normal material line will warp under load for laminated composite plates, leading to three-dimensional deformations that generate complex stress states. To overcome this problem, several high-order, reined plate theories have been proposed. While these approaches work well for some cases, they often lead to inefficient formulations because they introduce numerous additional variables. This paper presents a different approach to the problem: based on a finite element semi-discretization of the normal material line, plate equations are derived from three-dimensional elasticity using a rigorous dimensional reduction procedure.

In structural analysis, many components are approximated as plates. More often that not, classical plate theories, such as Kirchhoff or Reissner-Mindlin plate theories, form the basis of the analytical developments. The advantage of these approaches is that they leads to simple kinematic descriptions of the problem: the plate's normal material line is assumed to remain straight and its displacement field is fully defined by three displacement and two rotation components. While such approach is capable of capturing the kinetic energy of the system accurately, it cannot represent the strain energy adequately. For instance, it is well known from three-dimensional elasticity theory that the normal material line will warp under load for laminated composite plates, leading to three-dimensional deformations that generate complex stress states. To overcome this problem, several high-order, reined plate theories have been proposed. While these approaches work well for some cases, they often lead to inefficient formulations because they introduce numerous additional variables. This paper presents a different approach to the problem: based on a finite element semi-discretization of the normal material line, plate equations are derived from three-dimensional elasticity using a rigorous dimensional reduction procedure.

In structural analysis, many components are approximated as plates. More often that not, classical plate theories, such as Kirchhoff or Reissner-Mindlin plate theories, form the basis of the analytical developments. The advantage of these approaches is that they leads to simple kinematic descriptions of the problem: the plate's normal material line is assumed to remain straight and its displacement field is fully defined by three displacement and two rotation components. While such approach is capable of capturing the kinetic energy of the system accurately, it cannot represent the strain energy adequately. For instance, it is well known from three-dimensional elasticity theory that the normal material line will warp under load for laminated composite plates, leading to three-dimensional deformations that generate complex stress states. To overcome this problem, several high-order, reined plate theories have been proposed. While these approaches work well for some cases, they often lead to inefficient formulations because they introduce numerous additional variables. This paper presents a different approach to the problem: based on a finite element semi-discretization of the normal material line, plate equations are derived from three-dimensional elasticity using a rigorous dimensional reduction procedure.

The twist stiffness of single and double-wall corrugated board is analyzed using first order shear deformation (FOSD) theory. Results are compared to finite element analysis (FEA) and dynamic test data for a large range of torsion loaded rectangular board specimens. The FOSD approach and FEA employ a homogenized core. In addition, a structural finite element model was developed where the web core is represented by shell elements. According to FOSD analysis, the twist stiffness is linearly dependent on the transverse shear moduli of the web core along both principal directions of the core. Good agreement between the torsional stiffness predictions by analytical and numerical approaches and test results is found for the range of single and double-wall boards examined. The FOSD solution is significantly less computationally demanding than FEA, and appears viable for prediction of the twist stiffness of corrugated board.

This report derives an analytical model of a thin plate of infinite spatial extent stiffened by ribs that have a finite width. The governing equation is a flexural plate model that has an external load and is reinforced by an infinite number of equally spaced ribs. The Heaviside step function is used to load the rib forces onto the plate. A Fourier series then replaces the Heaviside step function and the equation decouples using an orthogonalization procedure. The resulting system can be represented by an infinite set of algebraic equations that are truncated to find a solution to the plate displacement. An example problem is formulated and the results are discussed.

This paper develops a three-dimensional analytical model of a fluid-loaded acoustic coating affixed to a rib-stiffened plate. The system is loaded by a plane wave that is harmonic both spatially and temporally. The model begins with Navier-Cauchy equations of motion for an elastic solid, which produces displacement fields that have unknown wave propagation coefficients. These are inserted into stress equations at the boundaries of the plate and the acoustic coating. These stress fields are coupled to the fluid field and the rib stiffeners with force balances. Manipulation of these equations develops an infinite number of indexed equations that are truncated and incorporated into a global matrix equation. This global matrix equation can be solved to determine the wave propagation coefficients. This produces analytical solutions to the systems' displacements, stresses, and scattered pressure field. This model, unlike previously developed analytical models, has elastic behavior and thus incorporates higher order wave motion that makes it accurate at higher wave numbers and frequencies. An example problem is investigated for three specific model results: (1) the dynamic response, (2) a sonar array embedded in the acoustic coating, and (3) the scattered pressure field. An expression for the high frequency limitation of the model is derived. It is shown that the ribs can have a significant impact on the structural acoustic response of the system., Published in the Journal of Sound and Vibration v329 p4192-4211, Apr 2010.

This report develops an analytical model that incorporates an infinite number of periodically spaced discrete masses into the equations of elasticity of a two-dimensional solid. Two specific problems are addressed. The first is that of a plate with the masses on the bottom edge, and the second is that of a plate with the masses embedded in the medium. the equations of elasticity are transformed into stress field expressions with the appropriate boundary conditions in the wave number-frequency domain. These equations are indexed using an integer shift property to obtain expressions of the higher-order dynamics of the system. Once this is accomplished, all the indexed equations of the system are written together in a single matrix equation. The problem is then solved using a truncated set of terms. The model results are compared to previously available low frequency results for solutions involving the flexural wave in the plate. A numerical example is then solved at high frequency that includes higher-order wave motion, and these results are discussed., The original document contains color images. Funding No. N00014-04-WX-2-0567.

This report derives an exact analytical expression of the shear coefficient in the Mindlin plate equation. The Mindlin plate equation is set equal to the thick plate equation, and the result is a closed-form expression of the shear coefficient at all wavenumbers and frequencies. A numerical example is included to show the variation of the shear coefficient. It is shown that the shear coefficient is extremely dependent on wavenumber and only slightly dependent on frequency. Shear coefficients derived in other work are compared favorably to the values calculated by this new method at the plate flexural wave response., The original document contains color images. All DTIC reproductions will be in black and white.

In structural analysis, many components are approximated as plates. More often that not, classical plate theories, such as Kirchhoff or Reissner-Mindlin plate theories, form the basis of the analytical developments. The advantage of these approaches is that they leads to simple kinematic descriptions of the problem: the plate’s normal material line is assumed to remain straight and its displacement field is fully defined by three displacement and two rotation components. While such approach is capable of capturing the kinetic energy of the system accurately, it cannot represent the strain energy adequately. For instance, it is well known from three-dimensional elasticity theory that the normal material line will warp under load for laminated composite plates, leading to three-dimensional deformations that generate complex stress states. To overcome this problem, several high-order, refined plate theories have been proposed. While these approaches work well for some cases, they often lead to inefficient formulations because they introduce numerous additional variables. This paper presents a different approach to the problem: based on a finite element semi-discretization of the normal material line, plate equations are derived from three-dimensional elasticity using a rigorous dimensional reduction procedure.

In structural analysis, many components are approximated as plates. More often that not, classical plate theories, such as Kirchhoff or Reissner-Mindlin plate theories, form the basis of the analytical developments. The advantage of these approaches is that they leads to simple kinematic descriptions of the problem: the plate’s normal material line is assumed to remain straight and its displacement field is fully defined by three displacement and two rotation components. While such approach is capable of capturing the kinetic energy of the system accurately, it cannot represent the strain energy adequately. For instance, it is well known from three-dimensional elasticity theory that the normal material line will warp under load for laminated composite plates, leading to three-dimensional deformations that generate complex stress states. To overcome this problem, several high-order, refined plate theories have been proposed. While these approaches work well for some cases, they often lead to inefficient formulations because they introduce numerous additional variables. This paper presents a different approach to the problem: based on a finite element semi-discretization of the normal material line, plate equations are derived from three-dimensional elasticity using a rigorous dimensional reduction procedure.

In structural analysis, many components are approximated as plates. More often that not, classical plate theories, such as Kirchhoff or Reissner-Mindlin plate theories, form the basis of the analytical developments. The advantage of these approaches is that they leads to simple kinematic descriptions of the problem: the plate’s normal material line is assumed to remain straight and its displacement field is fully defined by three displacement and two rotation components. While such approach is capable of capturing the kinetic energy of the system accurately, it cannot represent the strain energy adequately. For instance, it is well known from three-dimensional elasticity theory that the normal material line will warp under load for laminated composite plates, leading to three-dimensional deformations that generate complex stress states. To overcome this problem, several high-order, refined plate theories have been proposed. While these approaches work well for some cases, they often lead to inefficient formulations because they introduce numerous additional variables. This paper presents a different approach to the problem: based on a finite element semi-discretization of the normal material line, plate equations are derived from three-dimensional elasticity using a rigorous dimensional reduction procedure.

In this report the behaviour of paper reinforced plastics known as High Pressure Laminates, HPL, is studied. The material is regarded as anisotropic. Young’s modulus, Poisson’s ratio, shear modulus and the in-plane moisture elongations are measured. Calculation of moisture induced deformations and forces are carried out, both for beam and plate theory.

The composite floor slab, which is composed of cast-in-place concrete and casting floor formworks, is assumed to be a double layered floor slab. This floor slab is proposed as ARC (Automation-oriented Reinforced Concrete Constructions) floor systems. Using the equivalent flexural rigidity for the double layered floor slabs consisting of two different elastic moduli, analytical solutions expressed in Fourier series by thin plate theory and by elementary beam theory can be easily applied to the composite floor slabs. As a result of this analytical investigation, elastic deflection and stress resultants of the composite floor slabs are discussed in this paper. And the calculation charts on deflection and stress resultants of the floor slab are prepared for the purpose of structural design on the composite floor slabs.

The composite floor slab, which is composed of cast-in-place concrete and casting floor formworks, is assumed to be a double layered floor slab. This floor slab is proposed as ARC (Automation-oriented Reinforced Concrete Constructions) floor systems. Using the equivalent flexural rigidity for the double layered floor slabs consisting of two different elastic moduli, analytical solutions expressed in Fourier series by thin plate theory and by elementary beam theory can be easily applied to the composite floor slabs. As a result of this analytical investigation, elastic deflection and stress resultants of the composite floor slabs are discussed in this paper. And the calculation charts on deflection and stress resultants of the floor slab are prepared for the purpose of structural design on the composite floor slabs.

A C degrees (penalty) finite element is developed for the equations governing the heterogeneous laminated plate theory of Yang, Norris and Stavsky. The YNS theory is a generalization of Mindlin's theory for homogeneous, isotropic plates to arbitrarily laminated anisotropic plates and includes shear deformation and rotary inertia effects. The present element can also be used in the analysis of thin plates by appropriately specifying the penalty parameter. A variety of problems are solved, including those for which solutions are not available in the literature, to show the material effects and the parametric effects of plate aspect ratio, length-to-thickness ratio, lamination scheme, number of layers and lamination angle on the deflections, stresses, and vibration frequencies. Despite its simplicity, the present element gives very accurate results. (Author)

Earlier work is improved and extended to provide formulas for the maximum tensile stress in the lid-to-wall seal, the maximum lid deflection, and the lid collapsing pressure for a rectangular flat pack under external pressure. It is shown how these formulas can facilitate (a) the proper design of the package so that it will retain its hermeticity and serviceability under a given screening pressure, and (b) the selection of a proper pressure to use in the hermeticity screening of an already designed package. Information is also given in the approximate equivalence of external pressure and centrifuge acceleration in regard to the seal stresses and lid behavior. Finally, experimental data on package hermeticity are presented, which tend to confirm the validity of the main hypotheses of the present work. (Author)

The forced extensional vibrations of paltes is investigated within the framework of the Kane-Mindlin theory for the high frequency extensional vibrations of isotropic elastic plates. The solution to problems with time dependent surface and boundary conditions is determined according to Williams' method. The resulting equations are applied to the forced extensional vibrations of infinite plate strips with clamped edge conditions. Numerical results for a shear loading are presented.

The influence of membrane effects on container sidewall behaviour, and the influence of transverse shear deformation on container floor behaviour, are evaluated by analysing several particular examples using appropriate plate theories. It is shown that consideration of membrane effects is essential for single skin sidewalls but not for cellular sidewalls. Transverse shear deformation is shown to have a measurable effect on floor deflexions, but its influence on stresses is negligible., The influence of membrane effects on container sidewall behaviour, and the influence of transverse shear deformation on container floor behaviour, are evaluated by analysing several particular examples using appropriate plate theories. It is shown that consideration of membrane effects is essential for single skin sidewalls but not for cellular sidewalls. Transverse shear deformation is shown to have a measurable effect on floor deflexions, but its influence on stresses is negligible.