The mathematics of finite elements and applications: proceedings of the Brunel University conference of the Institute of Mathematics and Its Applications held in April 1972, ed

The Mathematics of Finite Elements and Applications provides information pertinent to the mathematics of finite elements, applications, algorithms, and computational techniques. This book discusses the developments in the mathematics of finite elements. Organized into 32 chapters, this book begins with an overview of the basis of the finite element process as a general approximation tool. This text then examines the methods for obtaining bounds on the errors in finite element solutions to two-dimensional elliptic boundary value problems defined on simply connected polygonal regions. Other chapters consider the practical implementation of the Galerkin and the Rayleigh–Ritz methods to equations of importance to physics and engineering. This book discusses as well a fundamental investigation into the problem of convergence in the finite element method. The final chapter deals with an algorithm that is applicable to the analysis of arbitrary plane stress or plane strain configurations. This book is a valuable resource for numerical analysts, mathematical physicist, applied mathematicians, computer scientists, and engineers. Content: Front Matter, Page iii Copyright, Page iv Contributors, Pages v-vii Preface, Pages ix-x, J.R. WHITEMAN FINITE ELEMENTS—THE BACKGROUND STORY, Pages 1-35, O.C. ZIENKIEWICZ AN INTRODUCTION TO THE MATHEMATICS OF THE FINITE ELEMENT METHOD, Pages 37-58, A.R. MITCHELL SOME RECENT ADVANCES IN THE MATHEMATICS OF FINITE ELEMENTS, Pages 59-81, M. ZLÁMAL ERROR ANALYSIS OF FINITE ELEMENT METHODS WITH TRIANGLES FOR ELLIPTIC BOUNDARY VALUE PROBLEMS, Pages 83-112, R.E. BARNHILL, J.R. WHITEMAN ORDERS OF CONVERGENCE IN FINITE ELEMENT METHODS, Pages 113-129, P.G. CIARLET FINITE ELEMENTS WITH HARMONIC INTERPOLATION FUNCTIONS, Pages 131-142, VIGGO HOPPE VARIATIONAL FINITE ELEMENT METHODS FOR INITIAL VALUE PROBLEMS, Pages 143-151, B. NOBLE A LEAST SQUARES FINITE ELEMENT SOLUTION OF NONLINEAR OPERATORS, Pages 153-162, J.E. AKIN THE l2 AND l∞ CONDITION NUMBERS OF THE FINITE ELEMENT STIFFNESS AND MASS MATRICES, AND THE POINTWISE CONVERGENCE OF THE METHOD, Pages 163-174, I. FRIED DUAL FORMULATIONS FOR POTENTIAL AND COMPLEMENTARY ENERGIES. UNILATERAL BOUNDARY CONDITIONS. APPLICATIONS TO THE FINITE ELEMENT METHOD, Pages 175-188, M. FREMOND GENERALISED MATRIX INVERSE TECHNIQUES FOR LOCAL APPROXIMATIONS OF OPERATOR EQUATIONS, Pages 189-199, Z. CSENDES, A. GOPINATH, P. SILVESTER FINITE ELEMENT SOLUTION OF UNSTEADY AND UNSATURATED FLOW IN POROUS MEDIA, Pages 201-211, J.C. BRUCH, G. ZYVOLOSKI SUFFICIENT CONDITIONS FOR CONVERGENCE IN THE FINITE ELEMENT METHOD FOR ANY SOLUTION OF FINITE ENERGY, Pages 213-224, C. PATTERSON COMBINED APPLICATION OF FINITE ELEMENT METHODS AND RICHARDSON EXTRAPOLATION TO THE TORSION PROBLEM, Pages 225-237, ULRICH HEISE FINITE ELEMENT APPLICATIONS IN MATHEMATICAL PHYSICS, Pages 239-282, J.T. ODEN A DYNAMIC ELASTOPLASTIC ANALYSIS OF THIN SHELLS OF REVOLUTION UNDER ASYMMETRIC MECHANICAL AND THERMAL LOADING, Pages 283-297, I.G. CAMERON ON HYBRID FINITE ELEMENTS, Pages 299-311, R.D. HENSHELL SOME FREE SURFACE TRANSIENT FLOW PROBLEMS OF SEEPAGE AND IRROTATIONAL FLOW, Pages 313-325, C.J. TAYLOR, P.W. FRANCE, O.C. ZIENKIEWICZ CALCULATION OF STRESS INTENSITY FACTORS AT CRACK TIPS USING SPECIAL FINITE ELEMENTS, Pages 327-336, W.S. BLACKBURN SINGULARITIES IN TRANSMISSION LINES, Pages 337-350, P. DALY APPLICATION OF THE FINITE ELEMENT METHOD TO THE EXTENSIONAL VIBRATIONS OF PIEZOELECTRIC PLATES, Pages 351-366, G.H. SCHMIDT VIBRATION OF CURVED STRUCTURES USING QUADRILATERAL FINITE ELEMENTS, Pages 367-378, M. PETYT, C.C. FLEISCHER ASSESSMENT OF ACCURACIES OF FINITE ELEMENT EIGENVALUES, Pages 379-386, A.V. KRISHNA MURTY, G. VENKATESWARA RAO FLEXIBILITY AND STIFFNESS MATRICES FOR AN OPEN-TUBE WARPING CONSTRAINT FINITE ELEMENT, Pages 387-399, G.B. BOLLAND A SANDWICH PLATE FINITE ELEMENT, Pages 401-413, A.J. BARNARD APPLICATION OF THREE-DIMENSIONAL FINITE ELEMENTS FOR ANALYSIS OF IRRADIATION-INDUCED STRESSES IN NUCLEAR REACTOR FUEL ELEMENTS, Pages 415-426, A. ALUJEVIC, J.L. HEAD THE ANALYSIS AND APPLICATION OF SPARSE MATRIX ALGORITHMS IN THE FINITE ELEMENT METHOD, Pages 427-447, D.J. EVANS THE COMPARISON OF ITERATIVE AND DIRECT SOLUTION TECHNIQUES IN THE ANALYSIS OF TIME-DEPENDENT STRESS PROBLEMS, INCLUDING CREEP, BY THE FINITE ELEMENT METHOD, Pages 449-462, A. JEZERNIK, A. LEECH A METHOD FOR SIMULATING CONCENTRATED FORCES AND LOCAL REINFORCEMENTS IN STRESS COMPUTATION, Pages 463-470, O. TINGLEFF SOME PRACTICAL SOLUTION TECHNIQUES FOR FINITE ELEMENT ANALYSIS, Pages 471-481, L.H. SEITELMAN ALGORITHM FOR THE LARGE DEFLECTION GEOMETRICALLY NONLINEAR PLANE AND CURVED STRUCTURES, Pages 483-494, A.C. LOCK, A.B. SABIR AUTOMATED SOLUTIONS OF TIME DEPENDENT PROBLEMS, Pages 495-506, W.C. CARPENTER, P.A.T. GILL AUTHOR INDEX, Pages 507-512 SUBJECT INDEX, Pages 513-520