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This book has one single purpose: to present the development of the partial hybrid finite element method for the stress analysis of laminated composite structures. The reason for this presentation is because the authors believe that partial hybrid finite element method is more efficient that the displacement based finite element method for the stress analysis oflaminated composites. In fact, the examples in chapter 5 of this book show that the partial hybrid finite element method is about 5 times more efficient than the displacement based finite element method. Since there is a great need for accurate and efficient calculation of interlaminar stresses for the design using composites, the partial hybrid finite method does provide one possible solution. Hybrid finite method has been in existence since 1964 and a significant amount of work has been done on the topic. However, the authors are not aware of any systematic piece of literature that gives a detailed presentation of the method. Chapters of the displacement finite element method and the evolution 1 and 2 present a sununary of the hybrid finite element method. Hopefully, these two chapters can provide the readers with an appreciation for the difference between the displacement finite element method and the hybrid finite element. It also should prepare the readers for the introduction of partial hybrid finite element method presented in chapter 3.
The purpose of this work is to develop global/local finite element models using partial hybrid stress finite elements for stress analysis of laminated composite structures. Based on the composite variational principle, the general formulations of partial hybrid single-layer finite element and multilayer finite element are presented. These formulations can be used to develop a series of partial hybrid finite elements. A 4-node degenerated plate element, an 8-node degenerated plate element, a 3-D, 8-node solid element, a 3-D, 20-node solid element, a 6-node transition element, a 15-node transition element, a multilayer solid element, and a multilayer transition element are presented. The elements developed in this thesis are examined by the, eigenvalue test to detect zero-energy deformation modes and the absence of rigid-body motion capability. The results show that the elements do not have any kinematic deformation modes, and they have a desired capability for rigid-body displacement. In addition, the non-zero eigenvalues of the element stiffness matrices are real and positive. In order to determine the optimal partial stress fields for the partial hybrid elements, a classification method of stress modes is presented. The method can be used to classify stress modes, select optimal stress modes, and set up an assumed stress matrix for a hybrid element. Also, the necessary and sufficient condition for avoiding spurious kinematic deformation mode is proposed and the optimal condition of an assumed stress field is presented. A computer program COMSA is developed to implement the partial hybrid finite element method. The Global/Local finite element models are established using plate element, solid element, and transition element. In the thesis, a few numerical examples are presented to verify the accuracy and efficiency of the finite element models. It has been shown that the global/local models using partial hybrid element are efficient and accurate for stress analysis of laminated composites due to the fact that they take advantage of the capacity of both 3-D elements and 2-D elements.
Composite materials are increasingly used in aerospace, underwater, and automotive structures. To take advantage of the full potential of composite materials, structural analysts and designers must have accurate mathematical models and design methods at their disposal. The objective of this monograph is to present the laminated plate theories and their finite element models to study the deformation, strength and failure of composite structures. Emphasis is placed on engineering aspects, such as the analytical descriptions, effective analysis tools, modeling of physical features, and evaluation of approaches used to formulate and predict the response of composite structures. The first chapter presents an overview of the text. Chapter 2 is devoted to the introduction of the definitions and terminology used in composite materials and structures. Anisotropic constitutive relations and Iaminate plate theories are also reviewed. Finite element models of laminated composite plates are presented in Chapter 3. Numerical evaluation of element coefficient matrices, post-computation of strains and stresses, and sample examples of laminated plates in bending and vibration are discussed. Chapter 4 introduces damage and failure criteria in composite laminates. Finally, Chapter 5 is dedicated to case studies involving various aspects and types of composite structures. Joints, cutouts, woven composites, environmental effects, postbuckling response and failure of composite laminates are discussed by considering specific examples.
While the theory and application of finite elements methods can be extended to incompatible, hybrid, and mixed element methods, important issues, such as determining the reliability of the solution of incompatible multivariable elements, along with a common perception of impracticality, have hindered the widespread implementation of these methods. Today, however, recent advances--many directly attributable to these authors--have allowed the development of the stability theory and abstract mathematics to useful tools. Hybrid and Incompatible Finite Element Methods introduces these advances in the theory and applications of incompatible and multivariable finite element methods. After an overview of the variation formulation of finite element methods in solid mechanics, the authors discuss the fundamental theory and systematically demonstrate the theoretical foundations of incompatible elements and their application to different problems in the theory of elasticity. They also introduce new ideas in the development of hybrid finite elements, study the numerical stability of the hybrid and mixed element, and establish the theory of zero energy deformation modes. The final chapters, explore applications to fracture problems, present a bound analysis for fracture parameters, and demonstrate an implementation of a finite element analysis program.
Advanced Finite Element Method in Structural Engineering systematically introduces the research work on the Finite Element Method (FEM), which was completed by Prof. Yu-qiu Long and his research group in the past 25 years. Seven original theoretical achievements - for instance, the Generalized Conforming Element method, to name one - and their applications in the fields of structural engineering and computational mechanics are discussed in detail. The book also shows the new strategies for avoiding five difficulties that exist in traditional FEM (shear-locking problem of thick plate elements; sensitivity problem to mesh distortion; non-convergence problem of non-conforming elements; accuracy loss problem of stress solutions by displacement-based elements; stress singular point problem) by utilizing foregoing achievements.
This book presents selected papers presented at the 8th International Conference "Design, Modeling and Experiments of Advanced Structures and Systems" (DeMEASS VIII, held in Moscow, Russia in May 2017) and reflects the modern state of sciences in this field. The contributions contain topics like Piezoelectric, Ferroelectric, Ferroelastic and Magnetostrictive Materials, Shape Memory Alloys and Active Polymers, Functionally Graded Materials, Multi-Functional Smart Materials and Structures, Coupled Multi-Field Problems, Design and Modeling of Sensors and Actuators, Adaptive Structures.
Ian, Theodore H.H. ;ASRL-TR-172-2DAAG46-73-C-0090DA-1-B-062113-A-661AMMRCCTR-73-40*Shells(Structural forms), *Plates, *Stresses, Composite materials, Laminates, Structural properties, Thermal stresses, Shear stresses, Deformation, Computer programs, Graphics, Curve fitting, Numerical integration, FORTRAN*Finite element analysis, *Structural analysis, FORTRAN 4 programming languageTwo methods of analyzing laminated- composite, linear-elastic plate and shell structures under transient mechanical and/or thermal loadings have been developed based on the hybrid-stress finite-element model. The computer codes corresponding to these two methods were also devel-oped and tested. Both programs are capable of treating thin or thick plates and shell structures. Shells with branches and cutouts can be treated. The outputs of the present computer programs are designed such that they can be easily adapted to any of the existing criteria for the strength of laminated composites. A SURVEY OF SUCH CRITERIA IS PRESENTED. (Author, modified-PL).