Students, whose presence throughout the
semester where insufficient to track their work, by academic waiver or other
causes, must also develop and present practices and tutored work for their
evaluation. The follow-up of this work shall be carried out in tutoring
sessions. In this case, the process of evaluation may include in addition to
the presentation of practices and tutored work, a practice session,
individually or in group, in which the student addresses manually or with the
computer the problems raised by the teacher. For the second chance you can present or improve
practices and tutored work. The tracking is done in tutorial sessions. The
assessment is done through presentation of practices and tutored work pending
and/or improved. The process of evaluation may include, in addition to the
presentation of practices and tutored work, a practical session, individually
or in group, in which the student addresses manually or with the computer the
problems posed by the teacher.

Learning outcomes	Study programme competences
Use the main laws of computational analysis of elastic solids and structures	A1 A23	B1 B2 B4 B5 B6 B7 B9	C4 C6
Solve exercises and problems in a reasoned and complete way	A1 A23	B1 B2 B4 B5 B6 B7 B9	C4 C6
Properly apply theoretical concepts in the laboratory. Make mathematical models of mechanical and structural systems	A1 A23	B1 B2 B4 B5 B6 B7 B9	C4 C6
Employ a correct language for the structural engineering field in order to show and to explain information and results		B1 B2 B4 B5 B6 B7 B9	C4 C6

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.

Methodologies / tests	Competencies	Ordinary class hours	Student’s personal work hours	Total hours
Laboratory practice	A1 A23 B1 B2 B4 B5 B6 B7 B9 C6 C4	4	24	28
Supervised projects	A1 A23 B1 B2 B4 B5 B6 B7 B9 C4 C6	16	28	44
Guest lecture / keynote speech	A1 A23 B1 B2 B4 B5 B6 B7 B9 C6 C4	18	45	63
Problem solving	A1 A23 B1 B2 B4 B5 B6 B7 B9 C6 C4	4	9	13

Personalized attention		2	0	2

(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students.

Methodologies	Description
Laboratory practice	Methodology that allows the realization of activities of practical character, with computer, such as modelization, analysis and simulation of mechanical and structural elements, as well as experimental studies in the workshop of structures, for studying its deformation and resistance
Supervised projects	Methodology designed to promote autonomous learning of students, solving a problem that involves the contents of the course and involves specific skills, under teacher supervision.
Guest lecture / keynote speech	Oral lecture supplemented with the use of audiovisual means, aiming transmit knowledge and facilitate the learning within the scope of structural analysis
Problem solving	Técnica a través da cal hai que resolver unha situación problemática específica, a partir da coñecemento que se traballou e que pode ter máis dunha solución.

Methodologies	Competencies	Description	Qualification
Laboratory practice	A1 A23 B1 B2 B4 B5 B6 B7 B9 C6 C4	Students must systematically attend practices. The proposed activities have to be done along the practical sessions, in order to be revised and evaluated by the teacher. The practices that aren’t developed during the practical classes, and periodically revised by the teacher will not be considered in the qualification. The evaluation process of the laboratory lessons includes a two hour practice session, where the student solves with the computer the problems proposed by the teacher, individually.	30
Supervised projects	A1 A23 B1 B2 B4 B5 B6 B7 B9 C4 C6	The projects include the theoretical and practical contents of the course. They are to be done individually. The projects will be developed during the practical sessions along the course and completed at home on the student personal work hours. The tasks will be followed and revised during the practical lessons. If the projects aren’t matured during the practical classes, nor periodically revised by the teacher, will not be considered in the qualification.	70

Assessment comments
<p class="MsoNormal">Students, whose presence throughout the semester where insufficient to track their work, by academic waiver or other causes, must also develop and present practices and tutored work for their evaluation. The follow-up of this work shall be carried out in tutoring sessions. In this case, the process of evaluation may include in addition to the presentation of practices and tutored work, a practice session, individually or in group, in which the student addresses manually or with the computer the problems raised by the teacher.</p><p class="MsoNormal"> </p><p class="MsoNormal">For the second chance you can present or improve practices and tutored work. The tracking is done in tutorial sessions. The assessment is done through presentation of practices and tutored work pending and/or improved. The process of evaluation may include, in addition to the presentation of practices and tutored work, a practical session, individually or in group, in which the student addresses manually or with the computer the problems posed by the teacher.</p>

Basic	R. Gutiérrez, E. Bayo, A. Loureiro, LE Romera (2010). Estructuras II. Reprografía del Noroeste. Santiago de Compostela Dassault Systèmes Simulia Corp. (2011). Abaqus Analysis User’s Manual. © Dassault Systèmes. Providence, RI, USA. Eugenio Oñate (1995). Calculo de estructuras por el método de elementos finitos. CIMNE, Barcelona, España Bathe K.J. (2006). Finite Elements Procedures.. Prentice-Hall, Pearson Education, Inc. USA

Complementary