Precursors of isogeometric analysis : finite elements, boundary elements, and collocation methods /: finite elements, boundary elements, and collocation methods. ([2019])

• Record Type: Book
• Further Information: Note: Christopher G. Provatidis.
• Authors: Provatidis, Christopher G
• Contents: Intro; Preface; Contents; Abbreviations; 1 Initial Attempts on CAD/CAE Integration; 1.1 The Conventional Meaning of Integrated CAD/CAE Systems; 1.2 The Meaning of CAD/CAE Integration Adopted in This Book; 1.3 CAD Interpolation; 1.4 CAE Methods; 1.4.1 Finite Element Method (FEM); 1.4.2 Boundary Element Method (BEM); 1.4.3 Collocation Method; 1.5 Modules of CAD/CAE Integration; 1.5.1 Mesh Generation; 1.5.2 Transfinite Elements; 1.5.3 Later Attempts; 1.6 Recapitulation and Some Historical Remarks; References; 2 Elements of Approximation and Computational Geometry 2.1 Description of Curve's Geometry as Well as of a Physical Quantity Along It2.2 Definitions; 2.3 Approximation Using Univariate Functions; 2.3.1 Taylor Power Series; 2.3.2 One-Dimensional Linear Interpolation; 2.3.3 One-Dimensional (1D) Piecewise Linear Interpolation; 2.3.4 One-Dimensional (1D) Lagrange and Power Series Interpolation; 2.3.5 One-Dimensional (1D) Hermite Interpolation; 2.3.6 One-Dimensional (1D) Nonrational Bézier Interpolation; 2.3.7 One-Dimensional (1D) Interpolation Using B-Splines; 2.4 Coons Interpolation Formula in Two Dimensions; 2.5 Gordon Interpolation Formula 2.6 Bézier Interpolation Formulas2.6.1 Nonrational Bézier Patch (Surface); 2.6.2 Rational Bézier Curve and Patch; 2.7 Interpolation Formula Using NURBS; 2.7.1 NURBS Curve; 2.7.2 NURBS Patch; 2.8 Barnhill's Interpolation Formula in a Parametric Triangular Domain; 2.8.1 Area Coordinates; 2.8.2 Derivation of Barnhill's Formula; 2.9 Recapitulation; References; 3 COONS' Interpolation as a Vehicle to Derive Large Isoparametric Elements; 3.1 General; 3.2 Small-Size Classical Finite Elements; 3.2.1 Four-Noded Element; 3.2.2 Eight-Noded Element 3.3 Global Shape Functions of Arbitrary Noded Coons Macroelement ("C-Element")3.3.1 General Formulation; 3.4 A Deeper Examination of Coons Interpolation and Relevant Coons Macroelements; 3.5 Trial Functions; 3.5.1 Piecewise Linear Trial Functions; 3.5.2 Lagrange Polynomials; 3.5.3 Natural Cubic B-Splines as Trial Functions; 3.6 Degeneration of Quadrilateral into a Triangular Patch; 3.7 Test Cases; 3.7.1 Potential Problems; 3.7.2 Application to Plane Elastostatics and Eigenanalysis; 3.7.3 Application to Plane Stress Transient Elastodynamics 3.7.4 Application to Problems of Axisymmetric Elasticity3.8 COONS Macroelement as a NURBS; 3.9 Recapitulation; References; 4 GORDON's Transfinite Macroelements; 4.1 General Formulation; 4.2 General Formulation; 4.3 A Structured Mesh of Bilinear Elements as a Special Case of Gordon Macroelement; 4.4 Lagrangian-Type Elements as a Special Case of Gordon Macroelement; 4.5 State-of-the-Art; 4.6 Test Problems; 4.7 Degenerated Triangular Transfinite Elements; 4.7.1 General; 4.7.2 Degenerated Quadrilateral with Four Nodes; 4.7.3 Degenerated Quadrilateral with Seven Nodes
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2019
• Extent: 1 online resource
• Subjects: 518/.25; Isogeometric analysis; Finite element method; Finite element method; Isogeometric analysis; Electronic books; Electronic books
• Languages: English
• ISBNs: 9783030038892; 3030038890
• Related ISBNs: 9783030038885; 3030038882
• Notes: Note: Includes bibliographical references and index.; Note: Description based on online resource; title from digital title page (viewed on February 18, 2019).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.