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Language | English |

Pages | 894 |

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# Structural Analysis with the Finite Element Method

## Structural Analysis with the Finite Element Method Contents

- SLENDER PLANE BEAMS. EULER-BERNOULLI THEORY
- COMPOSITE LAMINATED PLANE BEAMS
- THICK/SLENDER PLANE BEAMS. TIMOSHENKO THEORY
- 3D COMPOSITE BEAMS
- THIN PLATES. KIRCHHOFF THEORY
- THICK/THIN PLATES. REISSNER-MINDLIN THEORY
- COMPOSITE LAMINATED PLATES
- ANALYSIS OF SHELLS WITH FLAT ELEMENTS
- AXISYMMETRIC SHELLS
- CURVED 3D SHELL ELEMENTS AND SHELL STIFFNERS
- PRISMATIC STRUCTURES. FINITE STRIP AND FINITE PRISM METHODS
- PROGRAMMING THE FEM FOR BEAM, PLATE AND SHELL ANALYSIS IN MAT-fem

## Preface to Structural Analysis with the Finite Element Method

This e book enhances the content material of the first quantity: Structural Analysis wit the FEM. Foundation and solids (Springer/CIMNE, 2009).

The scope of the second quantity covers the finite ingredient evaluation of “structural components” equivalent to beams, plates and shells.

Equally, as in Quantity 1, the examine is restricted to linear static evaluation solely. The e book is addressed to undergraduate college students and readers which are uncovered to the FEM evaluation of beams, plates and shells for the first time. No earlier expertise on the FEM is strictly crucial.

Nonetheless, some information of fundamental FEM ideas, equivalent to mesh discretization, displacement interpolation, form capabilities, numerical integration, ingredient matrices and vectors, meeting of the stiffness equations, and many others., as described in Quantity 1, will facilitate the understanding of the underlying concepts behind the FEM.

All through the textual content emphasis has been put in the examine of beam, plate and shell constructions with composite laminated materials, this being a chance of accelerating curiosity for sensible purposes.

For didactic causes, nevertheless, the homogeneous and isotropic materials case is taken into account first, and normally in a separate chapter, with a purpose to facilitate the examine to an inexperienced reader.

As in Quantity 1, the examine of every structural mannequin is launched with the detailed description of the underlying concept.

This consists of the common structural mechanics assumptions, the kinematic description, the stress and stress fields, the constitutive relationship and the expression of the digital work precept by way of stress resultants and generalized strains outlined over the “reference geometry” of the ingredient, i.e. a line for a beam, a airplane for a plate or a flat shell and a curved floor for a common shell construction.

Chapter 1 introduces the FEM evaluation of two-dimensional (2D) airplane slender beams following the classical Euler-Bernoulli beam concept. The favored two-noded Euler-Bernoulli beam ingredient is derived in some element.

The chapter concludes with the formulation of two rotation-free beam components. These components have the vertical deflection as the solely nodal variable and are an fascinating various to straightforward slender beam components.

Chapter 2 describes the formulation of beam components based mostly on the extra superior Timoshenko beam concept. This concept accounts for the impact of shear deformation and is subsequently relevant to slender and thick beams.

Timoshenko beam components endure from the so-called shear locking defect that results in overstiff conditions for slender beams. Various procedures to keep away from shear locking are described.

Chapter 3 is dedicated to the FEM evaluation of beams with composite laminated materials. Emphasis is put in finding out the particularities launched by the composite materials in the mechanical behaviour of the beam, the extra essential one being the introduction of the axial deformation mode along with the commonplace bending mode typical of homogeneous airplane beams.

Greater order beam theories which are capable of reproduce the complexity of the in-plane displacement area throughout the thickness are described.

An efficient 2-noded composite laminated Timoshenko beam ingredient based mostly on the so-called refined zigzag concept is detailed.

Chapter 4 research three-dimensional (3D) Timoshenko and Euler-Bernoulli beams underneath arbitrary loading.

Each the classical Saint-Venant concept permitting for a uniform torsion area and the extra advanced concept for nonuniform torsion of beams with thin-walled open part are described.

Each theories are generalized for homogeneous and composite materials. Various two-noded beam components enough for every concept thought of are offered.

Chapter 5 focusses on the FEM evaluation of homogeneous skinny plates following the classical Kirchhoff plate concept.

The difficulties for satisfying the continuity situation for the deflection slopes throughout the ingredient sides are detailed.

Various conforming and non-conforming quadrilateral and triangular skinny plate components are offered. A part of the chapter is dedicated to the examine of two households of rotation-free skinny plate triangles.

Chapter 6 extends the FEM evaluation to thick and skinny homogeneous plates that comply with the extra superior Reissner-Mindlin plate concept.

This may be seen as an extension of Timoshenko beam concept and, thus, it accounts for transverse shear deformation results. Completely different methods to keep away from the shear locking defect are detailed.

A group of Reissner-Mindlin quadrilateral and triangular plate components is offered.

Chapter 7 is dedicated to composite laminated plates. The impact of the axial displacement induced by the adjustments in the materials properties throughout the thickness in the governing equations of the plate downside are detailed.

An correct 4-noded composite laminated plate quadrilateral based mostly on the refined zigzag concept is offered.

Chapter 8 introduces the FEM examine of shell constructions through flat shell components. The fundamental equations of Reissner-Mindlin flat shell concept expressed in the native axes of the ingredient are equivalent to these of a composite laminated plate as studied in the earlier chapter.

The equations for a flat shell ingredient are formulated for homogeneous and composite laminated materials.

The particularity of the meeting of the ingredient equations in international axes are detailed. The formulation of skinny shell components following Kirchhoff concept can also be defined.

The chapter concludes with the description of some larger order theories for composite laminated flat shell components, together with the refined zigzag concept.

Chapter 9 offers with axisymmetric shell constructions. Reissner-Mindlin assumptions for the shell kinematics are studied first.

Each homogeneous and composite laminated supplies are thought of. A easy locking-free 2-noded troncoconical axisymmetric shell ingredient is offered in some element.

The formulation of curved axisymmetric shell components can also be studied and the mixed impact of shear and membrane locking is mentioned.

The derivation of skinny axisymmetric shell components following Kirchhoff assumptions is defined and two fascinating rotation-free skinny axisymmetric shell components are offered.

The axisymmetric formulation is particularized for round plates, arches and shallow shells. The derivation of axisymmetric shell components through the degeneration of 3D axisymmetric stable components can also be defined.

The chapter concludes with the examine of upper order theories for composite laminated axisymmetric shells.

Chapter 10 research the evaluation of 3D shell constructions of arbitrary form utilizing degenerated stable components.

The degeneration course of is defined and the ingredient matrices and vectors are obtained.

Completely different methods for deriving degenerated shell components freed from shear and membrane locking are offered. A number of procedures for the express integration of the ingredient stiffness matrix throughout the thickness are defined.

The fundamental ideas of the isogeometry method and the derivation of isogeometric shell components are studied. The chapter concludes with the formulation of stiffened shell components by coupling beam and shell components.

Chapter 11 presents the derivation of finite strip and finite prism strategies for evaluation of prismatic plate/shell and 3D stable constructions, respectively.

These components mix a finite ingredient approximation throughout the transverse part of the construction with Fourier collection expansions for representing the longitudinal response.

Each procedures can subsequently be thought of as a specific class of decreased order fashions.

The finite strip formulation is detailed for plates, folded plates with straight and round plant and axisymmetric shells with non arbitrary loading.

The easy 2-noded strip permits one to investigate advanced prismatic shell constructions, equivalent to boxgirder bridges, in an very simple kind.

The finite prism formulation is derived for prismatic solids with straight and round plant and axysymmetric solids with arbitrary loading.

Chapter 12 explains the programming of a few of the components studied in the e book for beam, plate and shell evaluation utilizing MATLAB. The weather are carried out in the MAT-Fem code that may be freely downloaded from the internet.

The final construction of the code is defined in addition to the fundamental ideas for programming the stiffness matrix and the equal nodal power for the ingredient. The important elements of the MAT-Fem code are listed for every ingredient thought of.

I wish to categorical my gratitude to Dr. Francisco Z´arate who was answerable for writing the pc program Mat-fem offered in Chapter 12 and in addition undertook the job of scripting this chapter.

The content material of the e book is an expanded model of the course on Finite Element Analysis of Constructions which I’ve taught at the Faculty of Civil Engineering in the Technical College of Catalonia (UPC) since 1979.

I wish to categorical my due to my colleagues in the Division of Continuum Mechanics and Structural Analysis at UPC for his or her assist and cooperation over a few years.

Particular due to Profs. Benjam´ın Su´arez, Miguel Cervera and Juan Miquel, Drs. Francisco Z´arate and Daniel di Capua and Mr. Miguel Angel Celigueta with whom I’ve shared the educating of the talked about course throughout a few years.

Many examples included in the e book are the results of issues solved by teachers and analysis college students at UPC and CIMNE in cooperation with firms that are acknowledged in the textual content. I thank all of them for his or her contributions.

Particular due to the GiD staff at CIMNE for offering many footage proven in the e book. Many thanks additionally to my colleagues and workers at CIMNE for his or her cooperation and assist throughout so a few years that has made potential the publication of this e book.

Lastly, my particular due to Mrs. Mar´ıa Jes´us Samper from CIMNE for her wonderful work in the typing and modifying of the manuscript.

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