Showing papers on "Plate theory published in 1992"

Finite Element Analysis of Composite Laminates

Abstract: The partial differential equations governing composite laminates (see Section 2.4) of arbitrary geometries and boundary conditions cannot be solved in closed form. Analytical solutions of plate theories are available (see Reddy [1–5]) mostly for rectangular plates with all edges simply supported (i.e., the Navier solutions) or with two opposite edges simply supported and the remaining edges having arbitrary boundary conditions (i.e., the Levy solutions). The Rayleigh-Ritz and Galerkin methods can also be used to determine approximate analytical solutions, but they too are limited to simple geometries because of the difficulty in constructing the approximation functions for complicated geometries. The use of numerical methods facilitates the solution of these equations for problems of practical importance. Among the numerical methods available for the solution of differential equations defined over arbitrary domains, the finite element method is the most effective method. A brief introduction to the finite element method is presented in Section 3.2.

On a simple triangular reissner/mindlin plate element based on incompatible modes and discrete constraints

Abstract: In this paper the formulation of a new triangular element based on the Reissner/Mindlin plate theory is presented. The element has three nodes and three d.o.f. per node only. It is based on constant bending modes plus incompatible energy orthogonal higher order bending modes. The transverse shear effects are represented using the moment equilibrium and the constitutive equations. Discrete (collocation) shear constraints are considered on each side to relate the kinematical and the independent shear strains. The element has a proper rank, is completely locking free, passes all constant patch-tests exactly. The detailed numerical evaluation shows that the element, called DST-BK, is a robust and high-performance element for thick and thin plates.

An analytical and experimental investigation of flutter suppression via piezoelectric actuation

Abstract: The objective of this research was to analytically and experimentally study the capabilities of piezoelectric plate actuators for suppressing flutter. Piezoelectric materials are characterized by their ability to produce voltage when subjected to a mechanical strain. The converse piezoelectric effect can be utilized to actuate a structure by applying a voltage. For this investigation, a two-degree-of-freedom wind tunnel model was designed, analyzed, and tested. The model consisted of a rigid wing and a flexible mount system that permitted a translational and a rotational degree of freedom. The model was designed such that flutter was encountered within the testing envelope of the wind tunnel. Actuators made of piezoelectric material were affixed to leaf springs of the mount system. Command signals, applied to the piezoelectric actuators, exerted control over the damping and stiffness properties. A mathematical aeroservoelastic model was constructed by using finite element methods, laminated plate theory, and aeroelastic analysis tools. Plant characteristics were determined from this model and verified by open loop experimental tests. A flutter suppression control law was designed and implemented on a digital control computer. Closed loop flutter testing was conducted. The experimental results represent the first time that adaptive materials have been used to actively suppress flutter. They demonstrate that small, carefully placed actuating plates can be used effectively to control aeroelastic response.

Impact Response of Orthotropic Composite Plates Predicted from a One-Parameter Differential Equation

Abstract: This paper presents an approximate analytical solution for the dynamic response of an infinite specially orthotropic plate impacted by an impactor with a semispherical tip. Thus, the solution is valid for low mass impacts. The analysis is an extension and rederivation of a solution for isotropic plates proposed by Zener. The analysis assumes a Hertzian contact law and is based on Kirchhoff's plate equation. The plate response is expressed in terms of contact force, contact pressure, central displacement, central curvature, and size of the impact affected area. The response is computed from a dimensionless differential equation in time, which is only dependent on the inelasticity parameter lambda. Lambda is a function of the impact velocity and variables describing the impactor and the plate. For a given lambda, the response can be interpolated from the solution plots for a number of representativ e values of lambda. Results computed from the model are compared with published numerical analyses and a number of experiments, and a close agreement is noted. Finally, the analysis shows the time-dependent velocity of a flexural wave propagating from the impact center.

A Variational Approach to Three-Dimensional Elasticity Solutions of Laminated Composite Plates

Abstract: The displacements in a laminated composite are represented as products of two sets of unknown functions, one of which is only a function of the thickness coordinate and the other is a function of the in-plane coordinates (i.e., separation of variables approach), and the minimization of the total potential energy is reduced to a sequence of iterative linear problems. Analytical solutions are developed for cross-ply and angle-ply laminated composite rectangular plates. The solution for simply-supported cross-ply plates under sinusoidal transverse load reduces to that of Pagano. Numerical results for stresses and is placements for antisymmetric angle-ply laminates are presented. The three-dimensional elasticity solutions developed are important because they can be used to study the behavior of composite laminates, in addition to serving as reference for approximate solutions by numerical methods and two-dimensional theories.

Models of convection-driven tectonic plates: a comparison of methods and results

Abstract: Recent numerical studies of convection in the earth's mantle have included various features of plate tectonics. This paper describes three methods of modeling plates: through material properties, through force balance, and through a thin power-law sheet approximation. The results obtained are compared using each method on a series of simple calculations. From these results, scaling relations between the different parameterizations are developed. While each method produces different degrees of deformation within the surface plate, the surface heat flux and average plate velocity agree to within a few percent. The main results are not dependent upon the plate modeling method and herefore are representative of the physical system modeled.

A general methodology for deriving shear constrained Reissner‐Mindlin plate elements

Abstract: In this paper the necessary requirements for the good behaviour of shear constrained Reissner–Mindlin plate elements for thick and thin plate situations are re-interpreted and a simple explicit form of the substitute shear strain matrix is obtained. This extends the previous work of the authors presented in References 18 and 31. The general methodology is applied to the re-formulation of some well known quadrilateral plate elements and some new triangular and quadrilateral plate elements which show promising features. Some examples of the good behaviour of these elements are given.

The propagation characteristics of the plate modes of acoustic emission waves in thin aluminum plates and thin graphite/epoxy composite plates and tubes

Abstract: Acoustic emission was interpreted as modes of vibration in finite aluminum and graphite/epoxy plates. The `thin plate'' case of classical plate theory was used to predict dispersion curves for the two fundamental modes described by the theory and to calculate the shapes of flexural waveforms produced by a vertical step function loading. There was good agreement between the theoretical and experimental results for the aluminum. Composite materials required the use of a higher order plate theory (Reissner-Mindlin) combined with lamination theory in order to get good agreement with the measured velocities. Plate modes were shown to be useful for determining the direction of motion of a source. Thus, with a knowledge of the material, it may be possible to ascertain the type of the source. For example, particle impact on a plate could be distinguished from a crack growing in the plate. A high fidelity transducer was needed to distinguish the plate modes. After evaluating several types of transducers, a broadband ultrasonic transducer was found which satisfied the fidelity requirement and had adequate sensitivity over the 0.1 to 1 MHz range. The waveforms were digitized with a 5 MHz transient recorder. The dispersion curves were determined from the phase spectra of the time dependent waveforms. The aluminum plates were loaded by breaking a 0.5 mm. pencil lead against the surface of the plate. By machining slots at various angles to the plane of a plate, the direction in which the force acted was varied. Changing the direction of the source motion produced regular variations in the measured waveforms. Four composite plates with different laminate stacking sequences were studied. To demonstrate applicability beyond simple plates, waveforms produced by lead breaks on a thin-walled composite tube were also shown to be interpretable as plate modes. The tube design was based on the type of struts proposed for Space Station Freedom''s trussed structures.

Simplified theory for composite thin-walled beams

Abstract: The theory presented here is suitable for either open-section or closed-section beams of any shape, laminate stacking sequence, and boundary conditions. Under more general assumptions than those of Vlasov, the equilibrium equations consist of seven ordinary differential equations. Further, these seven equations were reduced to four coopled ordinary differential equations

On vibration and buckling of symmetric laminated plates according to shear deformation theories

Abstract: The frequency and buckling equations of rectangular plates with various boundary conditions are developed within the third-order and the first-order shear deformation plate theories. The third-order theories account for a quadratic distribution of the transverse shear strains through the thickness of the plate. In the first part of this paper, Levinson's third-order theory, derived as a special case from Reddy's third-order theory, is used to study a plate laminated of transversely isotropic layers. The relationship between the original form of the governing equations and the interior and the edge-zone equations of the plate is closely examined and the physical insights from the latter equations are established. In the second part of the paper, the first-order shear deformation theory and the third-order theory of Reddy are studied for vibration and buckling.

Non-linear finite strip analysis of rectangular laminates under end shortening, using classical plate theory

Abstract: The finite strip method is developed for predicting the geometrically non-linear response of rectangular composite laminates with simply supported ends when subjected to uniform end shortening in their plane. At the loaded ends lateral in-plane expansion may be allowed freely or may be prevented completely in different versions of the approach. The permitted laminate material properties are quite general, encompassing anisotropy and full coupling between in-plane and out-of-plane behaviour. The analysis is based on the use of the classical plate theory and the non-linearity is introduced in the strain-displacement equations in the manner of the von Karman assumptions. Three different types of finite strip are presented with either linear, quadratic or cubic interpolation of the membrane displacement components across a strip: in each case the bending displacement component varies cubically across a strip. Results are presented for isotropic plates and for unsymmetric cross-ply, angle-ply and arbitrary laminates.

An assumed-stress hybrid 4-node shell element with drilling degrees of freedom

Abstract: An assumed-stress hybrid/mixed 4-node quadrilateral shell element is introduced that alleviates most of the deficiencies associated with such elements. The formulation of the element is based on the assumed-stress hybrid/mixed method using the Hellinger-Reissner variational principle. The membrane part of the element has 12 degrees of freedom including rotational or 'drilling' degrees of freedom at the nodes. The bending part of the element also has 12 degrees of freedom. The bending part of the element uses the Reissner-Mindlin plate theory which takes into account the transverse shear contributions. The element formulation is derived from an 8-node isoparametric element by expressing the midside displacement degrees of freedom in terms of displacement and rotational degrees of freedom at corner nodes. The element passes the patch test, is nearly insensitive to mesh distortion, does not 'lock', possesses the desirable invariance properties, has no hidden spurious modes, and for the majority of test cases used in this paper produces more accurate results than the other elements employed herein for comparison.

Postbuckling of Shear Deformable Composite Flat Panels Taking Into Account Geometrical Imperfections

Abstract: The postbuckling behavior of composite flat panels subjected to uniaxial/biaxial compressive loads is investigated. To this end a refined geometrically nonlinear theory of composite plates is developed. The effects played by transverse shear deformation, initial geometric imperfections, the character of the in-plane boundary conditions and lamination are studied and a series of pertinent conclusions are outlined. Throughout the paper, the results obtained within the transverse shear deformable plate model are compared with their classical counterparts and conclusions related to their range of applicability are presented.

Analysis of Aircraft Structures: An Introduction

Abstract: Introduction to the second edition Introduction to the first edition Part I. The Fundamentals of Structural Analysis: 1. Stress in structures 2. Stresses and coordinate axis rotations 3. Displacements and strains 4. Strains in rotated coordinate systems 5. The mechanical behavior of engineering materials 6. Linearly elastic materials Part II. Introduction to the Theory of Elasticity: 7. The theory of elasticity 8. Plane stress theory of elasticity solutions Part I and Part II review questions Part III. The Engineering Theory for Straight, Long Beams: 9. Bending and extensional stresses in beams 10. Beam bending and extensional deflections 11. Additional beam bending topics 12. Uniform torsion of beams 13. Beam torsion approximate solutions Beam bending and torsion review questions 14. Beam shearing stresses due to shearing forces Part IV. Work and Energy Principles: 15. Work and potential energy principles Part V. Energy Based Numerical Solutions: 16. Precursor numerical analyses 17. Introduction to the finite element method 18. Finite element truss problems 19. Basic aspects of multidimensional finite elements 20. The unit load method for determinate structures 21. The unit load method for indeterminate structures Parts IV and V review Part VI. Extensions to Plate Theory and Finite Element Applications: 22. Thin plate theory 23. Elastic and aeroelastic instabilities Selected answers to Part I exercises Selected answers to Part II exercises Selected answers to Part III exercises Selected answers to Part IV and Part V exercises Selected answers to Part VI exercises References.

Nonlinear flutter of two-dimensional simply supported symmetric composite laminated plates

Abstract: The nonlinear flutter behavior of a two-dimensional simply supported symmetric composite laminated plate at high supersonic Mach number has been investigated. Yon Karman's large deflection plate theory and quasisteady aerodynamic theory have been employed. Galerkin's method has been used to reduce the governing equations to a system of nonlinear ordinary differential equations in time, which are then solved by a direct numerical integration method. Nonlinear flutter results are presented with the effects of aerodynamic damping, in-plane force, static pressure differential, and anisotropic properties. Results show that the anisotropic properties such as fiber orientation and elastic modulus ratio have significant effects on the behavior of both limit cycle oscillation and chaotic motion.

The electrohydrodynamic plume between a line source of ions and a flat plate-theory and experiment

Abstract: The electrohydrodynamic (EHD) flow between a line source of ions and a flat plate due to an electric field acting on an injected space charge is examined both theoretically and experimentally. A number of simplifying assumptions (e.g., laminar flow and negligible diffusion of charge) are made such that the governing equations are tractable. The mathematical model used is taken from heat transfer analysis and the experimental results are very close to theoretical ones. With such encouraging agreement it may be possible to present a more formal analogy between electroconvective and natural convection flows, leading to a more precise definition of the role of each parameter involved, as well as indicating methods of analysis for EHD problems. >

A quadrilateral hybrid‐Trefftz plate bending element for the inclusion of warping based on a three‐dimensional plate formulation

Abstract: A plate formulation, for the inclusion of warping and transverse shear deformations, is considered. From a complete thick and thin plate formulation, which was derived without ad hoc assumptions from the three-dimensional equations of elasticity for isotropic materials, the bending solution, involving powers of the thickness co-ordinate z, is used for constructing a quadrilateral finite plate bending element. The constructed element trial functions, for the displacements and stresses, satisfy, a priori, the three-dimensional Navier equations and equilibrium equations, respectively. For the coupling of the elements, independently assumed functions on the boundary are used. High accuracy for both displacements and stresses (including transverse shear stresses) can be achieved with rather coarse meshes for thick and thin plates.