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Preface; Contents; Chapter 1: Representation of Curves on a Plane; 1.1 Parametric Modeling of Polynomial Curve; 1.1.1 Polynomial Program List; 1.1.2 Understanding Parametric Modeling; 1.2 Bézier Curve; 1.2.1 BernsteinBasis Program List; 1.2.2 Bernstein Function List; 1.2.3 BezierCurve Program List; 1.2.4 What is a Basis Function?; 1.2.5 The Roles of a Control Point; 1.2.6 BezierCurveCP Program List; 1.2.7 Rational Bézier Curve; 1.2.8 RationalBezierBasis Program List; 1.2.9 RationalBezierCurve Program List; 1.2.10 What Is a Weight?; 1.2.11 Why Do We Need to Rationalize?; 1.3 B-spline Curve.
1.3.1 BsplineBasis Program List1.3.2 Bspline Function List; 1.3.3 BsplineCurve Program List; 1.3.4 BsplineCurveCP Program List; 1.3.5 The Roles of Knot Vector; 1.3.6 Rational B-Spline Curve; 1.3.7 RationalBsplineBasis Program List; 1.3.8 NURBS Curve; 1.3.9 NURBSBasis Program List; 1.3.10 Nurbs Function List; 1.3.11 NURBSCurveDrawCP Program List; 1.3.12 Derivatives of NURBS Basis Function; 1.3.13 DNURBSBasis Program List; 1.3.14 DNurbsLeibnitz Program List; References; Further Reading; Chapter 2: Numerical Integration; 2.1 Introduction; 2.2 Gauss-Legendre Quadrature.
2.3 Length, Jacobian Operator, and Radius of Curvature of a Curve2.3.1 Gaussquadrature Program List; 2.3.2 Legendre Function List; 2.4 Sinusoidal Curve Example; 2.4.1 Sinusoidalcurve Program List; Further Reading; Chapter 3: Finite Element Formulation of Beam Elements; 3.1 What Is a Finite Element?; 3.2 Beam Element in the Real World; 3.3 Beam in Finite Element Context; 3.4 Theory of Beams; 3.4.1 Straight Euler-Bernoulli Beam; 3.4.2 Straight Timoshenko Beam; 3.4.3 General Curved Euler-Bernoulli Beam; 3.4.4 General Curved Timoshenko Beam; 3.5 Governing Equations of Beam Elements.
3.5.1 Straight Euler-Bernoulli Beam3.5.2 Straight Timoshenko Beam; 3.5.3 General Curved Euler-Bernoulli Beam; 3.5.4 General Curved Timoshenko Beam; 3.6 Matrix Formulation of Euler-Bernoulli Beam; 3.6.1 Derivation of Shape Functions; 3.6.2 Governing Equation in Matrix Forms; 3.6.3 KMmatrixEBPoly Program List; 3.6.4 NshapeEBPoly Function List; 3.7 Matrix Formulation of Timoshenko Beam; 3.7.1 Derivation of Shape Functions; 3.7.2 Governing Equation in Matrix Forms; 3.7.3 KMmatrixTiPoly Program List; 3.7.4 NshapeTiPoly Function List; 3.8 Matrix Formulation of General Curved Euler-Bernoulli Beam.
3.8.1 Governing Equation in Matrix Forms3.9 Matrix Formulation of General Curved Timoshenko Beam; 3.9.1 Governing Equation in Matrix Forms; 3.10 Matrix Formulation of a Circular Curved Beam; 3.10.1 Exact Shape Functions; References; Further Reading; Chapter 4: Isogeometric Approach to Beam Element; 4.1 Introduction; 4.2 NURBS for Straight Beam Element Formulation; 4.2.1 Euler-Bernoulli Beam Element; 4.2.2 KMmatrixEBNURBS Program List; 4.2.3 Timoshenko Beam Element; 4.2.4 KMmatrixTiNURBS Program List; 4.3 NURBS for General Curved Beam Element Formulation.
1.3.1 BsplineBasis Program List1.3.2 Bspline Function List; 1.3.3 BsplineCurve Program List; 1.3.4 BsplineCurveCP Program List; 1.3.5 The Roles of Knot Vector; 1.3.6 Rational B-Spline Curve; 1.3.7 RationalBsplineBasis Program List; 1.3.8 NURBS Curve; 1.3.9 NURBSBasis Program List; 1.3.10 Nurbs Function List; 1.3.11 NURBSCurveDrawCP Program List; 1.3.12 Derivatives of NURBS Basis Function; 1.3.13 DNURBSBasis Program List; 1.3.14 DNurbsLeibnitz Program List; References; Further Reading; Chapter 2: Numerical Integration; 2.1 Introduction; 2.2 Gauss-Legendre Quadrature.
2.3 Length, Jacobian Operator, and Radius of Curvature of a Curve2.3.1 Gaussquadrature Program List; 2.3.2 Legendre Function List; 2.4 Sinusoidal Curve Example; 2.4.1 Sinusoidalcurve Program List; Further Reading; Chapter 3: Finite Element Formulation of Beam Elements; 3.1 What Is a Finite Element?; 3.2 Beam Element in the Real World; 3.3 Beam in Finite Element Context; 3.4 Theory of Beams; 3.4.1 Straight Euler-Bernoulli Beam; 3.4.2 Straight Timoshenko Beam; 3.4.3 General Curved Euler-Bernoulli Beam; 3.4.4 General Curved Timoshenko Beam; 3.5 Governing Equations of Beam Elements.
3.5.1 Straight Euler-Bernoulli Beam3.5.2 Straight Timoshenko Beam; 3.5.3 General Curved Euler-Bernoulli Beam; 3.5.4 General Curved Timoshenko Beam; 3.6 Matrix Formulation of Euler-Bernoulli Beam; 3.6.1 Derivation of Shape Functions; 3.6.2 Governing Equation in Matrix Forms; 3.6.3 KMmatrixEBPoly Program List; 3.6.4 NshapeEBPoly Function List; 3.7 Matrix Formulation of Timoshenko Beam; 3.7.1 Derivation of Shape Functions; 3.7.2 Governing Equation in Matrix Forms; 3.7.3 KMmatrixTiPoly Program List; 3.7.4 NshapeTiPoly Function List; 3.8 Matrix Formulation of General Curved Euler-Bernoulli Beam.
3.8.1 Governing Equation in Matrix Forms3.9 Matrix Formulation of General Curved Timoshenko Beam; 3.9.1 Governing Equation in Matrix Forms; 3.10 Matrix Formulation of a Circular Curved Beam; 3.10.1 Exact Shape Functions; References; Further Reading; Chapter 4: Isogeometric Approach to Beam Element; 4.1 Introduction; 4.2 NURBS for Straight Beam Element Formulation; 4.2.1 Euler-Bernoulli Beam Element; 4.2.2 KMmatrixEBNURBS Program List; 4.2.3 Timoshenko Beam Element; 4.2.4 KMmatrixTiNURBS Program List; 4.3 NURBS for General Curved Beam Element Formulation.