Condensed Isogeometric Analysis for Plate and Shell Structures 1st edition by Buntara Gan ISBN 0367023482 978-0367023485

Condensed Isogeometric Analysis for Plate and Shell Structures 1st edition by Buntara Gan ISBN 0367023482 978-0367023485

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ISBN 10: 0367023482
ISBN 13: 978-0367023485
Author: Buntara Gan 

Condensed Isogeometric Analysis for Plates and Shell Structures proposes a novel technique for plate and shell governing equations based on isogeometric analysis, which condenses the dynamic equilibrium equation for plate and shell structures―suitable for reducing the computation cost of large degrees of freedom due to the adoption of Non-Uniform Rational Basis Spline (NURBS) models in the plate and shell element formulations. It features useful guidance for understanding the isogeometric approach and includes accompanying MATLAB® source code in each chapter to deepen readers' understanding of the fundamental theories and methods of civil, architectural, and mechanical engineering.

Condensed Isogeometric Analysis for Plate and Shell Structures 1st Table of contents:

1. Representing a Surface Using Nonuniform Rationalized B-Spline

1.1 Parametric Modeling of a Surface

1.1.1 PolynomialSurface Program List

1.1.2 Understanding Parametric Modeling

1.1.3 Parametric Curve Program List

1.1.4 Parametric Surface Program List

1.2 Bézier Curve

1.2.1 BernsteinBasis Program List

1.2.2 Bernstein Function List

1.2.3 All about a Basis Function

1.2.4 The Roles of a Control Point

1.2.5 BezierCurveCP Program List

1.2.6 Rational Bézier Curve

1.2.7 RationalBezierBasis Program List

1.2.8 Weighting Parameter

1.2.9 Rationalization of Basis Functions

1.3 Bézier Surface

1.3.1 BezierSurface Program List

1.4 B-Spline Curve

1.4.1 BsplineBasis Program List

1.4.2 Bspline Basis Function List

1.4.3 Rational B-Spline Curve

1.5 NURBS Curve

1.5.1 The Interpretation of a Knot

1.5.2 NurbsBasis Program List

1.5.3 Nurbs Function List

1.5.4 NurbsCurveDrawCP Program List

1.6 NURBS Surface

1.6.1 NurbsBasisSurface Program List

1.6.2 NurbsSurfaceCP Program List

1.7 Derivatives of NURBS Curve

1.7.1 DNurbsBasis Program List

1.7.2 DNurbsLeibnitz Function List

1.8 Derivatives of NURBS Surface

1.8.1 NurbsSurface Function List

References

2. Numerical Integrations on a Surface

2.1 Numerical Integration

2.2 Gauss–Legendre Quadrature

2.2.1 GaussLegendreFunction Program List

2.2.2 Legendre Function List

2.3 Jacobian Operator of a Surface

2.4 Area Calculation of the Parametric Surface

2.4.1 ParametricSurfaceArea Program List

2.5 Area Calculation of the NURBS Surface

2.5.1 NurbsSurfaceArea Program List

2.6 Curvature and Gradient of the NURBS Surface

2.6.1 NurbsSurfaceCurvGrad Program List

References

3. Theory of Plate and Shell Elements

3.1 Theory of Plate and Shell

3.2 Shell Meant by a Thin Plate

3.3 Thin Plate Formulation

3.4 Governing Equations of Thin Plates

3.5 Navier Solutions for Rectangular Plates

3.5.1 Formulations for Bending Problem of Rectangular Plates

3.5.2 Solution for Bending of a Rectangular Plate Example

3.5.3 BendingPlateNavier Program List

3.5.4 Formulations for Free Vibration Problem of Rectangular Plates

3.5.5 Solution for Free Vibration of a Rectangular Plate Example

3.5.6 Formulations for Buckling Problem of Rectangular Plates

3.5.6.1 Case 1: Biaxial Compression of a Plate

3.5.6.2 Case 2: Biaxial Compression and Tension of a Plate

3.5.6.3 Case 3: Uniaxial Compression of a Rectangular Plate

3.5.7 Solution for Buckling Problem of a Rectangular Plate Example

References

4. Theories of Thick Plate and Shell Elements

4.1 Various Theories of Plate and Shell

4.2 Classical Plate Theory

4.3 First-Order Shear Deformation Theory

4.4 Third-Order Shear Deformation Theory

4.5 Higher Order Shear Deformation Theory

4.5.1 Polynomial Function-Based Models

4.5.2 Non-polynomial Function-Based Models

4.6 Simplified Theories

4.7 Mixed Theories

4.8 3D Elasticity

4.9 Unified Formulation

4.10 Shell Meant by a Thick Plate

4.11 Thick Plate and Shell Formulation

4.12 Governing Equations of Thick Plates

4.13 Navier Solutions for FSDT Rectangular Plates

4.13.1 Formulations for Bending Problem of Square FSDT Plates

4.13.2 Solution for Bending of a Square Plate Example

4.13.3 BendingPlateNavier Program List

4.13.4 Formulations for Free Vibration Problem of Square FSDT Plates

4.13.5 Solution for Free Vibration of a Square FSDT Plate Example

4.13.6 FreeVibrationPlateNavier Program List

4.13.7 Formulations for Buckling Problem of Square FSDT Plates

4.13.8 Solution for Buckling Problem of Square FSDT Plates

4.13.9 BucklingPlateNavier Program List

References

5. Finite Element Formulation for Plate and Shell

5.1 Finite Element for Solving the Governing Equations

5.2 Finite Element: An Explanatory Example

5.3 Plate and Shell in the Finite Element Context

5.4 Shape Function for a Kirchhoff Thin Plate Element

5.5 Governing Equation in Matrix Form

5.6 Gaussian Quadrature for Integrating the Matrices in FEM

5.7 Making the Stiffness and Mass Matrices of the Kirchhoff Plate Element

5.7.1 KMmatrixKirchhoffFEM Program List

5.7.2 NShapeKirchhoffFEM Function List

5.8 Shape Function for a Mindlin Thick Plate Element

5.9 Governing Equation in Matrix Form

5.10 Gaussian Quadrature for Integrating the Matrices in FEM

5.11 Making the Stiffness and Mass Matrices of the Mindlin Plate Element

5.11.1 KMmatrixMindlin Program List

5.11.2 NShapeMindlinConsistent Function List

References

6. Isogeometric Analysis for Plate and Shell

6.1 Isogeometric Analysis

6.2 NURBS for Plate and Shell Elements

6.3 NURBS for Kirchhoff Thin Plate Element

6.4 Making the Stiffness and Mass Matrices of the Kirchhoff Plate Element

6.4.1 KMmatrixKirchhoffNurbs Program List

6.4.2 NurbsSurface Function List

6.5 NURBS for Mindlin Thick Plate Element

6.6 Making the Stiffness and Mass Matrices of the Mindlin Plate Element

6.6.1 KMmatrixMindlinIGA Program List

References

7. Recoverable Sandwich Condensation

7.1 Condensation in Finite Element Method

7.2 Sandwich Condensation for Isogeometric Analysis

7.3 Static Condensation

7.4 Dynamic Condensation

7.5 Procedure of Condensation

7.6 Condensing the Stiffness and Mass Matrices of the Mindlin Plate Element

7.6.1 KMmatrixMindlinIGACondensed Program List

7.6.2 Condensation Function List

References

8. Square Flat Plate Example

8.1 Square Thick Flat Plate Analyzed Using Condensed Isogeometric Analysis

8.2 Static Problem

8.3 Free Vibration Problem

8.4 Flat Mindlin Plate Problem

8.4.1 FlatMindlinPlateProblem Program List

Reference

9. Free Surface Plate Example

9.1 Free Surface Plate Analyzed by Using Condensed Isogeometric Analysis

9.2 Static Problem

9.3 Free Vibration Problem

9.3.1 FreeSurfaceMindlinPlate Program List

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Tags: Buntara Gan, Condensed Isogeometric, Shell Structures