Structural Analysis with the Finite Element Method Linear Statics 1st Edition by Eugenio Onate ISBN 9048179718 9789048179718

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ISBN 10:    9048179718
ISBN 13: 978-9048179718
Author:   Eugenio Onate

STRUCTURAL ANALYSIS WITH THE FINITE ELEMENT METHOD

Linear Statics

Volume 1 : The Basis and Solids

Eugenio Oñate

The two volumes of this book cover most of the theoretical and computational aspects of the linear static analysis of structures with the Finite Element Method (FEM). The content of the book is based on the lecture notes of a basic course on Structural Analysis with the FEM taught by the author at the Technical University of Catalonia (UPC) in Barcelona, Spain for the last 30 years.

Volume1 presents the basis of the FEM for structural analysis and a detailed description of the finite element formulation for axially loaded bars, plane elasticity problems, axisymmetric solids and general three dimensional solids. Each chapter describes the background theory for each structural model considered, details of the finite element formulation and guidelines for the application to structural engineering problems. The book includes a chapter on miscellaneous topics such as treatment of inclined supports, elastic foundations, stress smoothing, error estimation and adaptive mesh refinement techniques, among others. The text concludes with a chapter on the mesh generation and visualization of FEM results.

The book will be useful for students approaching the finite element analysis of structures for the first time, as well as for practising engineers interested in the details of the formulation and performance of the different finite elements for practical structural analysis.

STRUCTURAL ANALYSIS WITH THE FINITE ELEMENT METHOD

Linear Statics

Volume 2: Beams, Plates and Shells

Eugenio Oñate

The two volumes of this book cover most of the theoretical and computational aspects of the linear static analysis of structures with the Finite Element Method (FEM).The content of the book is based on the lecture notes of a basic course onStructural Analysis with the FEM taught by the author at the Technical University of Catalonia (UPC) in Barcelona, Spain for the last 30 years.

Volume 2 presents a detailed description of the finite element formulation for analysis of slender and thick beams, thin and thick plates, folded plate structures, axisymmetric shells, general curved shells, prismatic structures and three dimensional beams. Each chapter describes the background theory for each structural model considered, details of the finite element formulation and guidelines for the application to structural engineering problems Emphasis is put on the treatment of structures with layered composite materials.

The book will be useful for students approaching the finite element analysis of beam, plate and shell structures for the first time, as well as for practising engineers interested in the details of the formulation and performance of the different finite elements for practical structural analysis.

Structural Analysis with the Finite Element Method Linear Statics 1st Table of contents:

1. SLENDER PLANE BEAMS. EULER-BERNOULLI THEORY

This section introduces the Euler-Bernoulli beam theory, which is fundamental for analyzing slender beams under bending. It covers:

• Basic Assumptions: Simplified conditions like small deflections and the neutral axis assumption.
• Displacement Field: The beam’s displacement behavior is modeled.
• Strain and Stress Fields: Defining how strain and stress vary along the beam.
• Moment-Curvature Relationship: The relation between bending moment and curvature.
• Principle of Virtual Work: A method to derive equilibrium equations.
• Beam Elements: Introduction of 2-noded Euler-Bernoulli beam elements with discretized equations for numerical analysis.
• Rotation-Free Elements: Specific beam elements that do not require rotation for better efficiency.

2. THICK/SLENDER PLANE BEAMS. TIMOSHENKO THEORY

This section covers the Timoshenko beam theory, which accounts for shear deformations, making it suitable for both thick and slender beams:

• Basic Assumptions and Strain Fields: Including transverse shear strain in addition to bending.
• Shear Locking: A phenomenon in numerical analysis where the shear deformation is overestimated. Various methods to avoid shear locking are discussed.
• Higher-Order Beam Elements: More sophisticated approaches to improve accuracy in numerical models.

3. COMPOSITE LAMINATED PLANE BEAMS

Focusing on beams made from multiple composite layers:

• Kinematics and Material Properties: Describes the deformation of laminated beams.
• Resultant Stresses: The combination of stresses from multiple layers.
• Generalized Constitutive Matrix: Relating stresses and strains.
• Failure Theories: Criteria for predicting failure under various loading conditions.
• Zigzag and Refined Theories: Advanced theories for more accurate results, especially for thick composite laminates.

4. 3D COMPOSITE BEAMS

This section expands to three-dimensional composite beams, analyzing both thin-walled and solid sections:

• Displacement and Strain Fields: Incorporating the effects of shear and torsion.
• Torsion and Warping: Important for analyzing thin-walled composite beams.
• Finite Element Discretization: Methods for creating 3D beam elements for numerical analysis.

5. THIN PLATES. KIRCHHOFF THEORY

Focuses on the classical Kirchhoff theory for thin plates:

• Assumptions and Stress-Strain Relations: Plate bending is assumed to be linear, with no transverse shear deformation.
• Finite Element Formulation: Various elements for plate bending analysis, such as 4-noded or 8-noded elements.

6. THICK/THIN PLATES. REISSNER-MINDLIN THEORY

This theory is used for thicker plates where shear deformation is significant:

• Strain and Stress Fields: Including transverse shear.
• Finite Element Analysis: Methods for handling thick plates with more accurate shear deformation effects.
• Performance Analysis: Examining the behavior of plate elements under different conditions, including shear locking.

7. COMPOSITE LAMINATED PLATES

Similar to the laminated beams section, but focused on plates:

• Theory and Computation: Analyzing layered composite plates using advanced theories.
• Failure and Delamination: Key aspects of composite material failure in plates.

8. ANALYSIS OF SHELLS WITH FLAT ELEMENTS

This section covers flat shell structures using various theories:

• Reissner-Mindlin Flat Shell Theory: For analyzing moderately thick shells.
• Shear and Membrane Locking: Techniques for avoiding numerical errors due to shear and membrane deformation.

9. AXISYMMETRIC SHELLS

Discusses shells with rotational symmetry, often used for structures like tanks or domes:

• Reissner-Mindlin and Kirchhoff Theories: Applied to axisymmetric shell analysis.
• Locking Issues: Solutions to issues that arise when modeling thick axisymmetric shells.

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