COMPUTER AIDED DESIGN OF MECHANICAL STRUCTURES
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- Versione italiana
- Academic year
- 2022/2023
- Teacher
- DENIS BENASCIUTTI
- Credits
- 6
- Didactic period
- Secondo Semestre
- SSD
- ING-IND/14
Training objectives
- The course aims to provide prospective engineers with the theoretical fundamentals, supported by practical examples, on computer assisted methods in mechanical structural analysis, with particular focus on matrix structural analysis and Finite Element Method (FEM). The practical examples show the use of computer codes, initially by MatLab software, then by a commercial finite element software.
The main skills learned in the course are:
- understanding the main concepts and technical terms used in the computer assisted mechanical analysis (stiffness matrix, assembly, shape function, isoparametric formulation, convergence analysis, shear locking);
- ability to define a numerical model that is most appropriate to solve a given mechanical analysis problem (choice of the element type, load and constraint conditions, symmetries, material model), regardless of the specific software used;
- ability to use a commercial finite element code to solve a mechanical analysis (creating the model, applying loads and constraints, solution, interpreting results);
- understanding some strategies for a critical interpretation of results output by a finite element software. Prerequisites
- No prerequisites are required.
It is however recommended to know the following topics:
- linear algebra and matrix analysis;
- theory of elasticity;
- basic knowledge of software MatLab. Course programme
- The course is schedule in 60 hours, with lectures (35 h) and laboratory exercises (25 h). The main topics addressed are:
1) MATRIX STRUCTURAL ANALYSIS:
Truss element: stiffness equation in local and global reference system (4 h). Characterisation of the structure, assembly of element stiffness matrices, expanded matrix (5 h), topology of the structure stiffness matrix (semi-bandwidth, skyline), application of the external loadings, constraints, solution of the structure system (4 h). Strain energy, Principle of Virtual Work, shape functions (3 h). Equivalent nodal forces due to shrink fit, temperature, concentrated and distributed load (2 h).
Beam element: Euler-Bernoulli and Timoshenko model, stiffness matrix (2 h).
Practical exercises with examples of truss/beam structures solved by MatLab and by a commercial finite element software (10 h).
2) FINITE ELEMENT METHOD (FEM)
Three-node triangular element (CST): interpolating functions, shape functions, compatibility and completeness, stiffness matrix, equivalent nodal forces of mechanical and thermal type (4 h). Assembly of element stiffness matrices, application of loads and constraints, solution (1 h). Axisymmetric three-node triangular element and six-node triangular element (LST) (2 h).
Four- and eight-node quadrangular elements (Q4, Q8), four-node tetrahedral element (2 h). Defects of CST and Q4 elements (shear locking) (2 h). Isoparametric formulation: mapping, jacobian matrix, Gauss integration (full, reduced), Barlow points, element distortion (2 h). Nonlinear analysis: methods of Newton-Raphson (full, modified) and arc length, elasto-plastic material (cinematic and isotropic model), contact problems, master/slave concept (2 h).
Practical exercises with use of a commercial finite element code for the structural analysis of bidimensional and three-dimensional components; import of CAD model as neutral file and subsequent defeaturing (15 h). Didactic methods
- The course is composed by lectures and laboratory exercises, in which numerical examples are carried out by MatLab software and a commercial finite element code.
Learning assessment procedures
- The correct understanding of the main course topics will be checked by:
1) written exam: several exercises (usually: one exercise on matrix structural analysis, one exercise on description of MatLab scripts, one on finite element modelling, one with questions on theory);
2) oral exam: questions on the main topics addressed in the course, and possibly a practical examination on the use of the finite element programs used during the practical examples in the course.
In order to be admitted at the oral exam, the written exam must achieve at least a positive mark (=18). The final mark will be calculated, in general, as the average between written and oral examinations. Reference texts
- Lecture notes given by the teacher.
Textbooks for further study:
- A. Gugliotta, A. Somà, N. Zampieri. Elementi Finiti. Quine Editore, 2022 (ISBN: 978-8831284066)
- D.S. Malkus, M.E. Plesha, R.J. Witt, R.D. Cook. Concepts and applications of finite element analysis. 4th edition. New York: Wiley& Sons, 2001.
- K.J. Bathe. Finite element procedures element analysis, 2nd edition. Editore: Klaus Jurge Bathe 2015.
- O.C. Zienkiewicz, R.L. Taylor. The Finite Element Method for solid and structural mechanics. Butterworth-Heinemann, 2005.
