Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates

Preface Introduction 1. Fluid field equations and modal analysis in rigid containers 2. Linear forced sloshing 3. Viscous damping and sloshing suppression devices 4. Weakly nonlinear lateral sloshing 5. Equivalent mechanical models 6. Parametric sloshing (Faraday's waves) 7. Dynamics of liquid sloshing impact 8. Linear interaction of liquid sloshing with elastic containers 9. Nonlinear interaction under external and parametric excitations 10. Interactions with support structures and tuned sloshing absorbers 11. Dynamics of rotating fluids 12. Microgravity sloshing dynamics Bibliography Index.

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Liquid Sloshing Dynamics

This work is an overview of available theories and finite elements that have been developed for multilayered, anisotropic, composite plate and shell structures. Although a comprehensive description of several techniques and approaches is given, most of this paper has been devoted to the so called axiomatic theories and related finite element implementations. Most of the theories and finite elements that have been proposed over the last thirty years are in fact based on these types of approaches. The paper has been divided into three parts. Part I, has been devoted to the description of possible approaches to plate and shell structures: 3D approaches, continuum based methods, axiomatic and asymptotic two-dimensional theories, classical and mixed formulations, equivalent single layer and layer wise variable descriptions are considered (the number of the unknown variables is considered to be independent of the number of the constitutive layers in the equivalent single layer case). Complicating effects that have been introduced by anisotropic behavior and layered constructions, such as high transverse deformability, zig-zag effects and interlaminar continuity, have been discussed and summarized by the acronimC
 -Requirements. Two-dimensional theories have been dealt with in Part II. Contributions based on axiomatic, asymtotic and continuum based approaches have been overviewed. Classical theories and their refinements are first considered. Both case of equivalent single-layer and layer-wise variables descriptions are discussed. The so-called zig-zag theories are then discussed. A complete and detailed overview has been conducted for this type of theory which relies on an approach that is entirely originated and devoted to layered constructions. Formulas and contributions related to the three possible zig-zag approaches, i.e. Lekhnitskii-Ren, Ambartsumian-Whitney-Rath-Das, Reissner-Murakami-Carrera ones have been presented and overviewed, taking into account the findings of a recent historical note provided by the author. Finite Element FE implementations are examined in Part III. The possible developments of finite elements for layered plates and shells are first outlined. FEs based on the theories considered in Part II are discussed along with those approaches which consist of a specific application of finite element techniques, such as hybrid methods and so-called global/local techniques. The extension of finite elements that were originally developed for isotropic one layered structures to multilayerd plates and shells are first discussed. Works based on classical and refined theories as well as on equivalent single layer and layer-wise descriptions have been overviewed. Development of available zig-zag finite elements has been considered for the three cases of zig-zag theories. Finite elements based on other approches are also discussed. Among these, FEs based on asymtotic theories, degenerate continuum approaches, stress resultant methods, asymtotic methods, hierarchy-p,_-s global/local techniques as well as mixed and hybrid formulations have been overviewed.

Theories and Finite Elements for Multilayered, Anisotropic, Composite Plates and Shells

Mixed and hybrid methods

For the prebuckling range an extensive literature of effective solution techniques exists for the numerical solution of structural problems but only a few algorithms have been proposed to trace nonlinear response from the pre-limit into the post-limit range. Among these are the simple method of suppressing equilibrium iterations, the introduction of artificial springs, the displacement control method and the “constant-arc-length method” of Riks/Wempner. It is the purpose of this paper to review these methods and to discuss the modifications to a program that are necessary for their implementation. Selected numerical examples show that a modified Riks/Wempner method can be especially recommended.

Strategies for Tracing the Nonlinear Response Near Limit Points

An examination of the variational formulations confirms the similarity between the incompatible displacement model and the assumed stress hybrid model that was pointed out by Irons in 1972. But the basic differences between the two are also identified. For 8-node solid elements the assumed stress terms obtained through a rational procedure also agree with those deduced by Irons purely from his physical insight.

Relations between incompatible displacement model and hybrid stress model

In view of the increasing interest in using composite materials for aerospace structures, the analysis of layered anisotropic plates becomes essential. The so-called classical laminated-plate theory (CPT) does not include effects of shear deformation. Recent elasticity solutions [ 1, 2, 3] of laminated plates show the importance of the transverse shear effects. While analytical solutions are usually restricted to problems with simple loading and boundary conditions, the finite-element method is found attractive in dealing with complicated problems. To include the effects of transverseshear deformation, the rotation of surface normal for different layers of a laminated plate must be considered as different. This has been found to be not feasible by the conventional finite-element displacement method [4]. The above-mentioned difficulties can be avoided if a hybrid-stress finite-element model is used [5, 6, 7]. In this paper, a general quadrilateral multilayer plate element is derived using the hybrid-stress method. The transverse shear effects, as well as the coupling effects of stretching and bending, are included. A comparison of results with known solutions is made and excellent accuracy in predicting both displacements and stresses is observed.

Finite Element Solutions for Laminated Thick Plates

: The condition of stability of the finite-difference equation for the transient response of a 'moderately thick' plate is derived. The effect of transverse shear and rotatory inertia on the stability condition are examined. For the same size of space increment the stability condition for a moderately thick plate requires a much smaller time increment than the corresponding one for a 'thin' plate in order to insure numerical stability. It is found that when either the effect of transverse shear or rotatory inertia is included, the sufficient stability condition is identical to that for the thin plate. (Author)

Stability of transient solution of moderately thick plate by finite-difference method

Exact solution of certain problems by finite- element method.

1 Margolis, M. and Leondes, C., "A parameter tracking servo for adaptive control systems," Air Force Office of Scientific Research TN 59-917 (August 1959). 2 Shipley, P. P., Engel, A. G., and Hung, J. W., "Self adaptive flight control by multivariable parameter identification," Air Force Flight Dynamics Lab. TR-65-90 (August 1965). k Puri, C. and Weygandt, N., "Transfer function tracking and adaptive control systems," Inst. Radio Engrs. Trans. Autom. Control AC-6,162-167 (May 1961). 4 Miller, B. J., "A general method of computing system parameters with an application to adaptive control," Am. Inst. Elec. Engrs., Paper 62-96 (January 1962). 5 Adams, J. J. and Bergeron, H. P., "Measurements of human transfer function with various model forms," NASA TN D-2394 (August 1964). 6 Ornstein, G. N., "Applications of a technique for the automatic analog determination of human response equation parameters," North American Inc., Columbus, Ohio, Rept. NA 61 H-l (January 2, 1961). 7 Graupe, K. K., "The analog solution of some functional analysis problems," Transactions on Communications and Electronics (American Institute of Electrical Engineers, New York, 1961), Vol. 79, Pt. I, pp. 793-799. 8 Rucker, R. A., "Real time system identification in the presence of noise," Proceedings, Western Electronics Convention, Paper 2.3 (August 1963). 9 Narendra, K. S. and McBride, L. E., "Multi-parameter self-optimizing systems using correlation techniques," Inst. Elec. Electron. Engrs. Trans. Autom. Control AC-9, 31-38 (January 1964). 10 Hahn, W., Theory and Application of Liapunov's Direct Method (Prentice Hall Inc., Englewood Cliffs, N. J., 1963). 11 LaSalle, J. P., "Asymptotic stability criteria," Proceedings of Symposia in Applied Mathematics (American Mathematical Society, Providence, R. I., 1962), Vol. 13. 12 McRuer, D. T. and Ashkenas, I. L., "Competing flight control systems for entry glider lateral control," Aeronautical Systems Div. TDR-62-699 (February 1964). 13 Cesari, L., Asymptotic Behavior and Stability Problems in Ordinary Differential Equations (Academic Press Inc., New York, 1963). 14 Hofmann, L. G., Lion, P. M., and Best, J. J. "Theoretical and experimental research on parameter tracking systems," Systems Technology Inc., Hawthorne, Calif., TR 148-1 (October 1965).

Pin Tong

Papers

Relations between incompatible displacement model and hybrid stress model

Finite Element Solutions for Laminated Thick Plates

Stability of transient solution of moderately thick plate by finite-difference method

Exact solution of certain problems by finite- element method.

Liquid motion in a circular cylindrical container with a flexible bottom.