# krainaksiazek nonlinear analysis of rectangular laminated plates 20124143

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### Geometrically non-linear analysis of layered composite plates and shells Politechnika Gdańska

**INŻYNIERIA MATERIAŁOWA**

This monograph includes the results of investigations carried out by the author since 1992. The whole period was divided into several research intervals of a different intensity. It all started during the author participation in the DFG-Research Project "Theory and Nonlinear FEM-Analysis of Elastic and Elasto-Plastic Anisotropic Structures Including Material Damage" performed under a supervision of Prof. Dieter Weichert and Dr-Ing. Rüdiger Schmidt at the University of Wuppertal, Germany in the period of 1991-1993r). Concurrently to, and to some extend separately from the main subject of the DFG project a scientific cooperation with Dr-Ing. Rüdiger Schmidt was initiated that was devoted to the FEM implementation of the Moderate Rotation Theory of anisotropic shells proposed by Schmidt and Reddy [426]. First versions of computer programs for the geometrically nonlinear analysis of layered shells were prepared by the author already in Wuppertal. The results of this period of research were presented in two conference reports (Bödefeld et al. [70], Kreja and Schmidt [263]) and one journal paper (Kreja et al. [269]). After his return to the Gdansk University of Technology in 1993 the author continued the research searching for possible improvements in the accuracy of the results by including additional terms in strain-displacement relations, improving procedures of the rotation update (Kreja and Schmidt [265]) and exploring assumed natural strain approach (Kreja and Schmidt [264]). After several months of break related to the intensive involvement in other research projects the author returned to the investigations on large deformations of anisotropic shells resulted in a computer implementation of the large rotation theory of anisotropic shells proposed by Librescu [290]. The results of that research activity were presented at several international conferences (Ferro et al. [165], Kreja [260], Kreja and Schmidt [266, 267]) and in one journal paper Kreja and Schmidt [268]. The present report starts with an extensive literature survey on the main concepts of theoretical models for multi-layered plates and shells. Then a systematic construction of a computational model is presented for a large rotation analysis of elastic laminated shells including a Finite Element Method implementation of the proposed algorithm. An essential part of the present report is devoted to the examination on the relevance of various approximation decisions in the large deformation analysis of plate and shell problems. A number of sample problems of non-linear, large rotation response of composite laminated structures are discussed. The report ends with a short summary of main conclusions and some recommendations for the potential areas of future research. The supplemented list of references contains 512 items cited in the text. Spis treści: PREFACE LIST OF SYMBOL AND ABBREVIATIONS 1. INTRODUCTION 1.1. Plates and shells - from Nature to space industry 1.2. Laminated composites and sandwich panels 1.3. Scope and objectives of this report 2. LITERATURE REVIEW AND MODELING CONSIDERATIONS 2.1. Development of theoretical models for plates and shells 2.2. Geometrically non-linear analysis of plates and shells 2.3. Theoretical models for layered thin-walled structures 2.4. Numerical implementation of plate and shell theories 2.5. Modeling considerations resulted from the presented review 3. INCREMENTAL FORMULATION OF NONLINEAR SHELL ANALYSIS 3.1. Incremental formulation 3.2. Shell geometry 3.3. Shell deformation 3.4. Strain-displacement relations 3.5. Virtual work principle 3.6. Constitutive relations 4. FINITE ELEMENT METHOD IMPLEMENTATION 4.1. Finite element discretization of the problem 4.2. Incremental equilibrium equations of FE model 4.3. Solving of incremental equilibrium equations 4.4. Finite elements used in this study 4.5. Computer implementation of the proposed FEA algorithm 4.6. Assessment of selected elements in linear analysis 5. LARGE DEFORMATION ANALYSIS EXAMPLES 5.1. Instability of clamped-hinged circular arches 5.2. Clamped laminated shallow arch under point load 5.3. Hinged laminated cylindrical panels under point load 5.4. Glass-epoxy cylinder under internal pressure 5.5. Asymmetric cross-ply simply supported plate strip 5.6. Clamped laminated cylindrical panels under point load 5.7. Stretching of an open cylinder 5.8. Pinched hemispherical shell with 18° hole 5.9. Axial compression of composite cylindrical panel 5.10. Buckling of composite cylindrical panels with square cut-outs 6. CONCLUSIONS AND FUTURE PERSPECTIVES 6.1. Concluding Remarks 6.2. Original Contribution 6.3. Recommendations and Future Perspectives ACKNOWLEDGEMENTS DEDICATION REFERENCES SUMMARY IN ENGLISH SUMMARY IN POLISH

Sklep: ksiegarnia.edu.pl

### Analysis of Plates Alpha Science International Ltd.

**Inne książki**

This book deals with the classical plate theory most commonly used for the analysis of thin metallic plate structures. The basic assumptions of the plate theory are not straightaway taken for granted but are deduced as logical inferences from a three-dimensional elasticity solution for a thin rectangular slab. In addition the elasticity results are used to verify the accuracy of the plate theory. Statics dynamics as well as stability of plates are dealt with. Besides a lucid explanation of the theory exact and approximate solution methodologies are discussed. The approach adopted throughout--with emphasis on close correspondence with the three-dimensional theory of elasticity and on the implications of each assumption of the plate theory--enables the reader to easily progress on to the study of state-of-the-art topics such as geometric and material nonlinearities refined plate theories accounting for warping and stretching of the normal and laminated construction and material orthotropy typical of fibre-reinforced composites.

Sklep: Albertus.pl

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