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Teaching GuideTerm Higher Polytechnic University College |
| Grao en Enxeñaría Mecánica |
 Subjects |
| FEM of Structures |
| Contents |
| Identifying Data | 2019/20 | |||||||||||||
| Subject | FEM of Structures | Code | 730G03069 | |||||||||||
| Study programme |
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| Descriptors | Cycle | Period | Year | Type | Credits | |||||||||
| Graduate | 1st four-month period |
Fourth | Optional | 6 | ||||||||||
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| Topic | Sub-topic |
| Chapter 0. The following topics develop the contents set up in the verification memory. | The finite element method; structural elements; numerical analysis of structures by means of computer programs. Mechanics of soil and foundations. |
| Chapter 1. Formulation of the Finite Element Method FEM for the static problem | Formulation of the structural static problem. Principle of virtual displacements. Discretization. Interpolation. Stiffness matrix and Load vector. Assembly. Transformation of element local and structure global degrees of freedom. |
| Chapter 2. Formulation of the FEM for the dynamic problem | Formulation of the structural dynamic problem. Mass and damping matrices. Imposition of displacement boundary conditions. Master and sleeve degrees of freedom. Displacement, deformation and stress fields |
| Chapter 3. Approximating element displacement field | Classification of various elastic problems. Generalized stress-strain matrices. Interpolation functions for generalized coordinate finite element family. Lagrange and Serendip elements. Lagrange interpolation. Convergence criteria of FEM. Parcel test |
| Chapter 4. Isoparametric elements | Introduction. Isoparametric elements. Geometric and natural coordinate system. Finite elements with a variable number of nodes. |
| Chapter 5. Isoparametric elements for plain stress and plain strain. | Plain stress and plain strain elastic problem. Formulation of an isoparametric element for plain stress. Jacobian matrix of isoparametric transformation. Singularities. Discretization errors. Mass and stiffness matrices. |
| Chapter 6. Computational issues. | Numerical integration. Method of Newton-Cotes. Gauss quadrature. Two-dimensional and three-dimensional integration. Full integration, reduced integration, selective integration. Recommendations for the type and order of integration. Construction of the numerical stiffness matrix of two-dimensional isoparametric linear element. Volume and surface load vectors. Thermal loads. Convergence criteria for isoparametric elements. |
| Chapter 7. Beam structural elements | Introduction. Euler-Bernoulli beam theory, Timoshenko beam theory. Equilibrium equations of beams. Formulation of the Hermitian beam finite element. Two-dimensional beam element. Three-dimensional beam element |
| Chapter 8. Plate and Shell elements | Behaviour of elastic plates. Kirchhoff plate theory. Reissner-Mindlin plate theory. Formulation of a finite element for plates. Equilibrium equations. Behaviour of elastic Shells. A flat Shell finite element. |
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