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    Mechanics of functionally graded material structures / Isaac Elishakoff, Demetris Pentaras and Cristina Gentilini.

    By: Elishakoff, Isaac [author.]Contributor(s): Pentaras, Demetris [author.] | Gentilini, Cristina [author.]Material type: TextTextPublisher: Singapore : World Scientific Publishing Company, [2016]Copyright date: ©2016Description: (xv, 323 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceSubject(s): Structural analysis (Engineering) | Functionally gradient materials | TECHNOLOGY & ENGINEERING / Civil / General | Functionally gradient materials | Structural analysis (Engineering)Genre/Form: Electronic books.Additional physical formats: No titleDDC classification: 624.1/7 LOC classification: TA645 | .E54 2016
    Contents:
    Table of Contents; Preface; Part I Three-Dimensional Analysis of Rectangular Plates Made of Functionally Graded Materials; Introduction; 1. Elastic Plates; 1.1 Bi-dimensional theories; 1.1.1 The CPT; 1.1.2 Shear deformation theories: First-order deformation theory; 1.1.3 Shear deformation theories: Third-order deformation theory; 1.2 Three-dimensional theory; 1.3 Some remarks; 2. Introduction to Functionally Graded Materials; 2.1 Fabrication methods; 2.2 Modelling of the effective material properties; 2.2.1 The rule of mixtures; 2.2.2 The Mori-Tanaka model; 2.2.3 Self-consistent model.
    2.3 Some remarks3. Dynamic Analysis of Plates Made of Functionally Graded Materials; 3.1 Statement of the problem; 3.1.1 Basic definitions; 3.2 Three-dimensional analysis; 3.2.1 Strain energy; 3.2.2 Kinetic energy; 3.2.3 Dissipation functional; 3.2.4 Work done by the external forces; 3.3 Ritz method: Displacement representation; 3.3.1 Chebyshev polynomials; 3.3.2 Boundary functions; 3.4 Solution methodology; 3.5 Numerical results; 3.5.1 Free vibrations; 3.5.2 Forced vibrations; 3.6 Some remarks; 4. Static Analysis of Plates Made of Functionally Graded Materials.
    4.1 Statement of the problem and solution methodology4.2 Numerical results; 4.3 Some remarks; Part II Vibration Tailoring of Inhomogeneous Beams and Circular Plates; 5. Beams Made of Functionally Graded Material; 5.1 Euler-Bernoulli beam equation; 5.2 Method of solution of uniform beam vibrations; 5.2.1 Determination of natural frequencies and mode shapes; 6. Vibration Tailoring of Inhomogeneous Elastically Restrained Vibrating Beams; 6.1 Background; 6.2 Analysis; 6.3 Comparison between closed-form solutions of inhomogeneous vibrating beam and homogeneous beam.
    6.4 Vibration tailoring: Numerical example7. Some Intriguing Results Pertaining to Functionally Graded Columns; 7.1 Background; 7.2 Formulation of the problem; 7.3 Dependence between 2 and P; 7.4 Numerical example; 7.5 Conclusion; 8. Design of Heterogeneous Polar-Orthotropic Clamped Circular Plates with Specified Fundamental Natural Frequency; 8.1 Background; 8.2 Derivation of governing differential equation; 8.3 Semi-inverse method of solution; 8.3.1 Parabolic mode shape; 8.3.2 Two cubic mode shapes; 8.3.3 Two alternative quartic mode shapes; 8.4 Discussion.
    8.5 Vibration tailoring: Numerical example9. Vibration Tailoring of Simply-Supported Polar Orthotropic Inhomogeneous Circular Plates; 9.1 Introduction; 9.2 Analysis; 9.2.1 Semi-inverse method of solution associated with m = 1; 9.2.2 Semi-inverse method of solution associated with m = 2; 9.2.3 Semi-inverse method of solution associated with m = 3; 9.2.4 Semi-inverse method of solution associated with m = 4; 9.3 Vibration tailoring: Numerical example; 10. Vibration Tailoring of Clamped-Clamped Polar Orthotropic Inhomogeneous Circular Plates; 10.1 Analysis.
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    		TA645 .E54 2016 (Browse shelf (Opens below)) 1 Available STACKS 51952000317906

    Online resource; title from PDF title page (EBSCO, viewed December 14, 2015).

    Includes bibliographical references and index.

    Table of Contents; Preface; Part I Three-Dimensional Analysis of Rectangular Plates Made of Functionally Graded Materials; Introduction; 1. Elastic Plates; 1.1 Bi-dimensional theories; 1.1.1 The CPT; 1.1.2 Shear deformation theories: First-order deformation theory; 1.1.3 Shear deformation theories: Third-order deformation theory; 1.2 Three-dimensional theory; 1.3 Some remarks; 2. Introduction to Functionally Graded Materials; 2.1 Fabrication methods; 2.2 Modelling of the effective material properties; 2.2.1 The rule of mixtures; 2.2.2 The Mori-Tanaka model; 2.2.3 Self-consistent model.

    2.3 Some remarks3. Dynamic Analysis of Plates Made of Functionally Graded Materials; 3.1 Statement of the problem; 3.1.1 Basic definitions; 3.2 Three-dimensional analysis; 3.2.1 Strain energy; 3.2.2 Kinetic energy; 3.2.3 Dissipation functional; 3.2.4 Work done by the external forces; 3.3 Ritz method: Displacement representation; 3.3.1 Chebyshev polynomials; 3.3.2 Boundary functions; 3.4 Solution methodology; 3.5 Numerical results; 3.5.1 Free vibrations; 3.5.2 Forced vibrations; 3.6 Some remarks; 4. Static Analysis of Plates Made of Functionally Graded Materials.

    4.1 Statement of the problem and solution methodology4.2 Numerical results; 4.3 Some remarks; Part II Vibration Tailoring of Inhomogeneous Beams and Circular Plates; 5. Beams Made of Functionally Graded Material; 5.1 Euler-Bernoulli beam equation; 5.2 Method of solution of uniform beam vibrations; 5.2.1 Determination of natural frequencies and mode shapes; 6. Vibration Tailoring of Inhomogeneous Elastically Restrained Vibrating Beams; 6.1 Background; 6.2 Analysis; 6.3 Comparison between closed-form solutions of inhomogeneous vibrating beam and homogeneous beam.

    6.4 Vibration tailoring: Numerical example7. Some Intriguing Results Pertaining to Functionally Graded Columns; 7.1 Background; 7.2 Formulation of the problem; 7.3 Dependence between 2 and P; 7.4 Numerical example; 7.5 Conclusion; 8. Design of Heterogeneous Polar-Orthotropic Clamped Circular Plates with Specified Fundamental Natural Frequency; 8.1 Background; 8.2 Derivation of governing differential equation; 8.3 Semi-inverse method of solution; 8.3.1 Parabolic mode shape; 8.3.2 Two cubic mode shapes; 8.3.3 Two alternative quartic mode shapes; 8.4 Discussion.

    8.5 Vibration tailoring: Numerical example9. Vibration Tailoring of Simply-Supported Polar Orthotropic Inhomogeneous Circular Plates; 9.1 Introduction; 9.2 Analysis; 9.2.1 Semi-inverse method of solution associated with m = 1; 9.2.2 Semi-inverse method of solution associated with m = 2; 9.2.3 Semi-inverse method of solution associated with m = 3; 9.2.4 Semi-inverse method of solution associated with m = 4; 9.3 Vibration tailoring: Numerical example; 10. Vibration Tailoring of Clamped-Clamped Polar Orthotropic Inhomogeneous Circular Plates; 10.1 Analysis.

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