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A finite-element formulation for a general triangular thin doubly-curved Kirchhoff shell element has been carried out, based upon the hybrid assumed stress variational model. This formulation is then applied specifically to conical (and cylindrical) shells, and the associated finite-element properties are evaluated. Several example static problems involving isotropic cylindrical shells and an isotropic conical shell subjected to mechanical loading are solved by employing the present triangular element to evaluate this formulation; good agreement with independent reliable solutions for these problems has been found. The formulation presented, however, also includes skew orthotropic plane stress shells, variable thickness shells, and thermal loads, all for linear elastic behavior. (Author).
~his Monograph has two objectives : to analyze a f inite e l e m en t m e th o d useful for solving a large class of t hi n shell prob l e ms, and to show in practice how to use this method to simulate an arch dam prob lem. The first objective is developed in Part I. We record the defi- tion of a general thin shell model corresponding to the W.T. KOlTER linear equations and we show the existence and the uniqueness for a solution. By using a co nform ing fi nite e l e m ent me t hod , we associate a family of discrete problems to the continuous problem ; prove the convergence of the method ; and obtain error estimates between exact and approximate solutions. We then describe the impl em enta t ion of some specific conforming methods. The second objective is developed in Part 2. It consists of applying these finite element methods in the case of a representative practical situation that is an arc h dam pro b le m. This kind of problem is still of great interest, since hydroelectric plants permit the rapid increase of electricity production during the day hours of heavy consumption. This regulation requires construction of new hydroelectric plants on suitable sites, as well as permanent control of existing dams that may be enlightened by numerical stress analysis .
The authors present a modern continuum mechanics and mathematical framework to study shell physical behaviors, and to formulate and evaluate finite element procedures. With a view towards the synergy that results from physical and mathematical understanding, the book focuses on the fundamentals of shell theories, their mathematical bases and finite element discretizations. The complexity of the physical behaviors of shells is analysed, and the difficulties to obtain uniformly optimal finite element procedures are identified and studied. Some modern finite element methods are presented for linear and nonlinear analyses. A state of the art monograph by leading experts.
A three node flat shell element with six engineering displacement degree-of-freedom at each node is developed. The basic formulation allows for the arbitrary location of the reference surface in which the membrane forces and bending moments are fully coupled. The well-known, highly accurate, DKT bending element is combined with a higher order membrane element in order to obtain a consistent formulation. The higher order membrane behavior is obtained by the introduction of three additional normal rotational degree-of-freedom. This report presents a summary of the theoretical steps involved in the development of the element. The accuracy of the element is illustrated by the solution of several standard problems and a comparison of results with other thin shell elements. (jes).
A finite element procedure is presented for solving thin shell problems of arbitrary geometry and boundary conditions. The actual smoothly curved shell surface is approximated by the assemblage of flat triangular plate elements. Both the membrance stiffness and plate bending stiffness of the flat element are considered and it is assumed that there is no coupling between these two types of element stiffness properties. The element stiffness properties are derived from assumed displacement functions, and triangle area coordinates are used for the derivation. A quadratic displacement function for the tangential displacements in the triangular element is assumed and the membrance stiffness is derived according to this assumed displacement function. A complete fourth order displacement function is used to derive the flexural stiffness of the triangular element. Shell or plate which is supported by edge beams or is stiffened by stiffeners is discussed. The twisting and axial stiffnesses, the eccentricity and the bending stiffness of the beam element are all considered. Various numerical examples are presented. These examples demonstrate the versatility and the accuracy given by the finite element procedure presented in this study. (Author).
The Finite Element Method: Its Basis and Fundamentals offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in the detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications. This edition sees a significant rearrangement of the book’s content to enable clearer development of the finite element method, with major new chapters and sections added to cover: Weak forms Variational forms Multi-dimensional field problems Automatic mesh generation Plate bending and shells Developments in meshless techniques Focusing on the core knowledge, mathematical and analytical tools needed for successful application, The Finite Element Method: Its Basis and Fundamentals is the authoritative resource of choice for graduate level students, researchers and professional engineers involved in finite element-based engineering analysis. A proven keystone reference in the library of any engineer needing to understand and apply the finite element method in design and development Founded by an influential pioneer in the field and updated in this seventh edition by an author team incorporating academic authority and industrial simulation experience Features reworked and reordered contents for clearer development of the theory, plus new chapters and sections on mesh generation, plate bending, shells, weak forms and variational forms