Showing papers on "Plate theory published in 1982"

Alternative ways for formulation of hybrid stress elements

Abstract: An element stiffness matrix can be derived by the conventional potential energy principle and, indirectly, also by generalized variational principles, such as the Hu-Washizu principle and the Hellinger-Reissner principle. The present investigation has the objective to show an approach which is concerned with the formulation of incompatible elements for solid continuum and for plate bending problems by the Hellinger-Reissner principle. It is found that the resulting scheme is equivalent to that considered by Tong (1982) for the construction of hybrid stress elements. In Tong's scheme the inversion of a large flexibility matrix can be avoided. It is concluded that the introduction of additional internal displacement modes in mixed finite element formulations by the Hellinger-Reissner principle and the Hu-Washizu principle can lead to element stiffness matrices which are equivalent to the assumed stress hybrid method.

Mixed formulation finite elements for mindlin theory plate bending

Abstract: Two new finite elements are developed for the Mindlin theory plate bending problem. The formulation is based on the modified Hellinger-Reissner principle with independent transverse shear strains. Numerical examples indicate that, with properly assumed transverse shear strains, these new elements designated as PLAT8 and PLAT8H do not exhibit locking effect even for very thin plates.

Vibration of Flexible Plate on Viscoelastic Medium

Abstract: The dynamic response of a massless flexible circular plate with a rigid core supported on a layered viscoelastic half-space and subjected to harmonic vertical and rocking excitation is studied. The mixed boundary-value problem for the case of relaxed contact conditions between the plate and the half-space is reduced to Fredholm integral equations of the second kind which are solved numerically. The effects of flexibility of the plate on the force-displacement relationship, on the motion of different points on the plate, and on the distribution of contact stresses beneath the plate are studied numerically. In general, it has been found that all of these aspects of the response of the plate are highly dependent on the flexibility of the plate relative to that of the supporting half-space.

Dynamic Response of Plate on Elastic Half-Space

Abstract: Analytical results are presented for the dynamic response of a plate bearing on an elastic half-space and subjected to harmonic forces. The present work represents a departure from existing analyses in that herein both the flexibility and three-dimensionality of the plate are taken into account. Displacements and contact stresses are presented for square plates having a practical range of flexural stiffness. The harmonic analysis is conducted within the framework of a global stiffness solution, in which the plate and subgrade impedance matrices are formulated independently in accordance with a prescribed discretization pattern. Then compatibility of displacements and equilibrium of forces are enforced at the plate-subgrade interface. Solutions are presented for massless square plates subjected to harmonic point, uniform pressure, and moment loadings. The effect of the plate's mass on its response is studied by starting with a perfectly flexible massive plate and subsequently increasing the stiffness toward the limit of a completely rigid plate.

Design Considerations for Silicon Circular Diaphragm Pressure Sensors

Abstract: The design of silicon circular-diaphragm pressure sensors was considered in order to develop highly-accurate pressure sensors. A relatively simple method of stress analysis was proposed. The anisotropy of the elastic properties of silicon, the large deflections of the plates, and elastic deformations of the support structures were taken into account in the stress analysis by the plate theory and the finite element method. Output voltages and their nonlinearities were calculated by applying stress analysis and piezoresistive sensor theories. The calculated results are in close agreement with the experimental results.

Strengthening of Single-Span Steel-Beam Bridges

Abstract: The use of post-tensioning to increase the strength of steel beams in beam and concrete-slab bridges is shown to be feasible. The purpose of the study is to determine a technique for increasing the capacity of the bridges to meet today's loadings. The results of testing a half-scale model of an existing bridge indicate that post-tensioning can be used with only minor deck cracking. Comparisons of the data from the model with results using orthotropic plate theory indicate that this theory can be used as a preliminary design methodology for determining the required prestress force and its location for strengthening existing bridges.

Hybrid stress finite element analysis of bending of a plate with a through flaw

Abstract: A hybrid stress finite element procedure for the solution of bending stress intensity factors of a plate with a through-the-thickness crack is presented. Reissner's sixth-order plate theory including the effects of transverse shear deformation is used. The dominant singular crack tip stress field is embedded in the crack tip singular elements and only regular polynomial functions are assumed in the far field elements. The stress intensity factors can be calculated directly from the crack tip singular stress solution functions. The effects of the plate thickness, the ratio between the crack size and the inplane dimension of the plate, and the singular element size on the stress intensity factor solution are investigated. The effects of the explicit enforcement of traction-free conditions along crack surfaces, which are the natural boundary conditions in the present hybrid stress finite element model, are also investigated. The numerical results of bending of a plate with a straight central crack compare favourably with analytical solutions. It is also found that the explicit enforcement of traction-free conditions along crack surfaces is mandatory to obtain meaningful results for the Mode I type of bending stress intensity factor.

Basic Principles of Plate Theory

Abstract: 1. Preliminaries.- 1.0 Motivation.- 1.1 Vectors-algebra.- 1.2 Vectors-calculus.- 1.3 Matrices.- 1.4 Statics-equilibrium.- 1.5 Summation convention and index notation.- 1.6 Elements of beam theory.- 1.7 Conclusions.- 2. Statics and Kinematics of Plate Bending.- 2.0 Introduction.- 2.1 The stress resultants.- 2.2 Principal values.- 2.3 The moment circle.- 2.4 Equilibrium equations-rectangular coordinates.- 2.5 Plate bending kinematics-rectangular coordinates.- 2.6 Equilibrium equations-polar coordinates-radial symmetry.- 2.7 Plate bending kinematics-polar coordinates-radial symmetry.- 2.8 Conclusions.- 3. Elastic Plates.- 3.0 Introduction.- 3.1 Elastic theory of plate bending-moment/curvature relations.- 3.2 Elastic theory of plate bending-governing equation.- 3.3 Circular plates-radial symmetry.- 3.4 Some simple solutions for circular plates.- 3.5 Simple solutions for problems in rectangular coordinates.- 3.6 Further separation of variable features-rectangular plates.- 3.7 Solution by finite differences.- 3.8 Some other aspects of plate theory.- 3.9 Stability of plates.- 3.10 Conclusions.- 4. Plastic Plates.- 4.0 Introduction.- A. Solid metal plates.- 4.1 Yield criteria.- 4.2 The bound theorems.- 4.3 The normality rule.- 4.4 Circular plates-square yield locus.- 4.5 Circular plates-Tresca yield locus.- 4.6 Plates of other shapes-square and regular shapes.- B. Reinforced concrete plates.- 4.7 Yield line theory-I. Fundamentals.- 4.8 Yield line theory-II. Further isotropic examples.- 4.9 Yield line theory-III. Orthotropic problems.- 4.10 Hillerborg strip theory.- 4.11 Conclusions.- 5. Optimal Plates.- 5.0 Introduction.- 5.1 Problem formulation.- 5.2 Constant curvature surfaces and principal directions.- 5.3 Basic results-corners.- 5.4 Some complete results.- 5.5 Moment volumes.- 5.6 Some theory.- 5.7 Conclusions.- 5.8 Exercises.- 6. Bibliography and Exercises.- 6.0 Bibliography.- 6.1 Exercises.- Appendix Geometry of Surfaces.- A.0 The need for geometry.- A.1 Geometry of a plane curve-curvature.- A.2 Length measurement on a surface-first fundamental form.- A.3 The normal to a surface.- A.4 Normal curvature-second fundamental form.- A.5 The derivatives of n-the Weingarten equations.- A.6 Directions on a surface.- A.7 The principal curvatures.- A.8 Principal directions.- A.9 Curvature and twist along the coordinate lines.- A.10 The curvature matrix.- A.11 The curvature circle.- A.12 Continuity requirements.- A.13 Special surfaces.- A.14 Summary-the geometrical quantities required for the construction of a plate theory.

Analysis of box-girder bridges by grillage and orthotropic plate methods

Abstract: The paper deals with the calculation of longitudinal moments and transverse shear in multi-spine box-girder bridges. Results from three-dimensional analyses by the well tested finite strip method a...

Effect of Transverse Shear Deformation on Anisotropic Plate Buckling

Abstract: Critical in-plane normal and shear loads of rectangular anisotropic laminated plates are presented. These were calculated using the shell code FASOR, which includes the effect of transverse shear deformation. For simply-supported orthotropic laminates with midplane symmetry normal buckling loads are verified by a closed-form solution derived from transverse shear deformation plate theory. Results are compared to previously pub lished solutions from three-dimensional elasticity theory and classical plate theory.

Analysis of composite girders with deformable connectors.

Abstract: In the case of a composite bridge beam, a perfect connection between the steel and concrete components exists only theoretically. In some types of connector design a rigid connection is achieved, others are more deformable and so a certain slip of the concrete deck with respect to the steel flange is inevitable. The problem is described as more severe when fewer connectors than the number required for full interaction are used. The influence of a deformable connection on the stress level and deflections of composite beams is investigated by the folded plate theory from which a versatile method of analysis is developed. Conclusions and recommendations for practical use of the method, derived from a parametric study, are also presented. (Author/TRRL)

Composite Defect Significance.

Abstract: : State of the art of defect criticality assessment in structural composite laminates has been summarized and significance of other ongoing programs has been reviewed through literature survey and organization of a limited attendance symposium on the subject. A number of tests have been performed to determine the range of validity of criticality criteria for disbonds in laminated beam and plate type structures, which were developed in previous related programs. Data correlation studies have shown the usefulness of linear elastic fracture mechanics approach, methods of stress analysis based on 2-D elasticity and modified laminated plate theories as well as semi-empirical growth laws for cyclic loading for assessing growth of disbonds under transverse shear. (Author)

Some problems of a plate bending hybrid model with shear effect

Abstract: A triangular plate bending hybrid element is constructed according to Reissner's principle. It has 9 degrees-of-freedom and the shear effect is included. The C0 formulation of thick plate is directly developed to solve the thin plate by imposing the discrete Kirchhoff constraints. The matching problem for bending and shear in the hybrid model of thick plate is effectively treated by use of the principle of the energy regulation such that the unified analysis of thick and thin plates is realized. Finally, numerical examples are presented.

Static Indentation Tests on Composite Plates for Impact Susceptibility Evaluation

Abstract: : Static indentation tests with spherical steel indenters were conducted on thin composite plates to assess the impact susceptibility of graphite epoxy composites. The data were used to validate an impact strength analysis based on large deflection plate theory. Tests and analysis were in good agreement on both plate stiffness and maximum strain energy at failure. A parametric analysis showed that for brittle matrix composites the matrix dominated the threshold of damage, while in tough matrix composites the fibers dominated the threshold of damage. Penetration was always dominated by large deflection membrane effects. (Author)

Axisymmetric Vibrations of Conical Shells with Variable Thickness

Abstract: In this paper, the axisymmetric free vibrations of truncated conical shells are analyzed by means of an improved shell theory. The equations of vibration and the boundary conditions are obtained from the stational condition of Lagrangian of the shells. The equations of vibration are solved exactly by a solution in series for a conical shell with linearly varied thickness along its axis and the effects of boundary conditions, thickness and semi-vertex angle on the natural frequencies are investigated. As a special case of the conical shell, we compare this theory with Mindlin's circular plate theory and with Mirsky's cylindrical shell theory.

Three-dimensional finite-element analysis of layered composite plates

Abstract: Results are presented for an investigation of the three-dimensional, geometrically nonlinear, finite-element analysis of the bending of laminated anisotropic composite plates. The individual laminae are treated as homogeneous, transversely isotropic, and linearly elastic. A fully three-dimensional isoparametric finite element with eight modes (i.e., linear element) and 24 degrees of freedom (three displacement components per node) is used. The numerical results obtained using this linear analysis are compared with the exact solutions given in Pagano (1969, 1970). It is found that the results of the linear analysis converge to the exact solution as the mesh is refined.

Elastic-plastic problem for a plate with a part-through crack under extension and bending

Abstract: In this paper a flat plate containing a relatively long and deep part-through crack and subjected to uniform membrane and bending loads is considered. It is assumed that the net ligament and the plate wall in some neighborhood of the crack are fully yielded. In analyzing the problem Reissner's Theory of plate bending is used. The plastic deformations are taken into account by using a plastic strip model. First some elastic results regarding the interaction of two collinear cracks are obtained. The crack opening displacement at various locations in the plate is then calculated for various crack sizes and stress ratios.

Advances and Trends in Plate Buckling Research.

Abstract: Advances and current trends in plate bucklin research are summarized. The field is divided into three parts: (1) classical buckling studies, including plates of rectangular, circular and other shapes; (2) classical complicating effects, including elastic foundation, anisotropic material, variable thickness, shear deformation and nonhomogeneous material; and (3) nonclassical considerations, including postbuckling, imperfections, parametric excitation, follower forces, magnetoelastic buckling and inelastic buckling.

The finite element analysis of thin-walled box spine-beam bridges

Abstract: This thesis considers the theoretical and experimental analysis of thin-walled box spine-beam bridges. Existing methods available for the analysis of spine-beam bridges have been reviewed, with special attention being paid to thin-walled box beam theories. A new approach combining the finite element technique and the thin-walled beamtheory, which is appropriate for design purposes, has been proposed. This approach is specially suitable for medium and long spans. It is intended to be a realistic and versatile method to be used during the preliminary analysis and design stage, when a full three-dimensional analysis is likely to be impractical. Special features related tothebending analysis of thin-walled members and the warping torsion theory of open and closed section members are summarized in the thesis. In addition, supplementary formulae for the calculation of the stress distributions and the thin-walled section properties are derived. The distortional effect on single-spined box beams subjected to torsion has been extended to a general form based on the principles of ordinary folded plate theory. A family of special one-dimensional sub-parametric elements has been developed. In addition to the usual truss and beam elements the family includes a general thin-walled box beam element which may be curved in space and may have a variable cross-section. Additional degrees of freedom have been included to account for the warping and distortion effects whichoccur in box beams. An inclined cable element with catenary action is included, and an approximate nonlinear process for the analysis of cablestayed bridges has been correlated with tests on an actual bridge structure. A finite element-grillage approach for the analysis of multibox structures with deformable sections has also been developed. The complete family of elements has been incorporated into a computer program called CUBAS. A supplementary program called PFRAN for calculating the distortional properties and the influence values of the equivalent Vierendeel frame has also been implemented. The accuracy of the results obtained is demonstrated by comparison with results obtained by other published methods. A series of model box beams were tested to •further substantiate the theoretical results. The model dimensions were chosen to highlight both warping and cross-sectional distortion effects. The degree of correlation obtained shows that the theoretical developments proposed in this thesis may be applied successfully to the analysis of box spine-beam bridges.

Stress concentration factors for cylindrically orthotropic plates

Abstract: Stress concentration factors are presented for circular holes in circular composite plates of cylindrical orthotropy when the outer edge of the plate is subjected to uniform uniaxial traction. The values that can be calculated from the formulas presented and the values shown in the diagrams are valid rigorously only for the circular plate but they can be used as approximation for differently shaped (for instance, rectangular) finite plates also.

Geometrically nonlinear analysis of layered composite shells

Abstract: Two kinds of finite-element analyses are developed for the geometrically nonlinear study of the large deformations in laminated composite structures, especially shells. The first kind of finite-element analysis utilizes the general incremental variational formulation as well as the total Lagrangian description of motion, and a three-dimensional degenerate element is adopted. The second kind of analysis employs a formulation based on deformable shell theory, and the plate-bending element is used. Numerical results for bending are presented for five plate and shell structures of isotropic as well as orthotropic composition, including an isotropic cylindrical panel with uniform loading and a laminated cylindrical panel with uniform loading. The results obtained using these analyses are found to be in good agreement with those available in the literature.

Finite Element Analysis of Cracked Plate Subjected to Out-of-plane Bending, Twisting and Shear

Abstract: A special crack element for the analysis of cracked plates subjected to out-of-plane bending, twisting and shear is developed based on a hybrid finite element model. Equilibrated stresses within a crack element are derived by making use of a complex variable method and Kirchhoff plate theory. An infinite plate containing a through crack subjected to transverse flexure is analyzed in order to investigate the accuracy of the stress intensity factor solutions, and the effects of element size and the number of stress parameters. The well-known analytical solutions for this problem are reexamined and correct solutions are provided. Other numerical examples include typical crack problems of a plate of finite dimensions under transverse flexure.

On the restricted torsion of narrow rectangular cross section by Kirchhoff's thin plate theory

Abstract: Kirchhoff's thin plate theory is used to solve the restricted torsion of narrow rectangular cross section as this problem is equivalent to the bending of a rectangular cantilever plate by a twisting moment at the free end. The results obtained not only prove the angle of twist obtained by Prof. Timoshenko using the energy method but give us stresses.