MAK510

School of Engineering \ Mechanical Engineering

3

9

Elective

Turkish

-

Direct stiffness matrix method. Finite element mesh, nodes and degrees of freedom, boundary conditions. Variational formulations of bar and plane beam elements. Planar stress problem. Triangular elements with three nodes for plane stress. Isoparametric elements. Shape functions. Convergence criteria. Finite element analysis with commercial software ABAQUS (and/or open source software Salome-Meca).

1. J. N. Reddy; An Introduction to the Finite Element Method, 3rd Ed, McGraw-Hill Education, 2005.
2. O. C. Zienkiewicz, R. L. Taylor; The Finite Element Method: Volume 1: The Basis, 5th Ed, Butterworth-Heinemann, 2000.
3. O. C. Zienkiewicz, R. L. Taylor; The Finite Element Method: Volume 2: Solid Mechanics, 5th Ed, Butterworth-Heinemann, 2000.
4. S. S. RAO; The Finite Element Method in Engineering, 5th Ed, Butterworth-Heinemann, 2010.
5. G. R. Liu, S. S. Quek; The finite element method: A Practical Course, Butterworth-Heinemann, 2003.

The main learning outcomes of this course are:
- understand the mathematical and physical foundations of the finite element method;
- understand the form function, parameter function and convergence criteria;
- gain the ability to solve engineering problems in the field of solid mechanics by finite element method;
- learn ABAQUS finite element method commercial software through example problems. To have an idea about other available commercial or open source software;
- To acquire the ability to write programs / codes related to finite element method, to reinforce existing knowledge in the field of programming.

1. Understand the mathematical and physical foundations of the finite element method;
2. Understand the form function, parameter function and convergence criteria;
3. Gain the ability to solve engineering problems in the field of solid mechanics by finite element method;
4. Learn ABAQUS finite element method commercial software through example problems. To have an idea about other available commercial or open source software;
5. To acquire the ability to write programs / codes related to finite element method, to reinforce existing knowledge in the field of programming.

Week 1: Introduction: Aim and scope of the course (Introduction, Ch_01).
Week 2: Basic mathematics: Matrices, matrix algebra (Matrix algebra and calculus, Appendices A, B, C, and D).
Week 3: The direct stiffness matrix method (The direct stiffness method, Ch_02, Ch_03).
Week 4: Finite element formulation of structural members (FE formulation of structural members, Ch_05).
Week 5: Finite element modeling: finite element mesh, nodes and degrees of freedom, loads, boundary conditions (Finite element modeling: mesh, loads, boundary conditions, Ch_06, Ch_07).
Week 6: Variational formulation of bar element (Variational formulation of bar element, Ch_11).
Week 7: Variational formulation of plane beam element (Variational formulation of plane beam element, Ch_12).
Week 8: The plane stress problem (The plane stress problem, Ch_14).
Week 9: Three-node plane stress triangles for plane stress (Three-node plane stress triangles, Ch_15).
Week 10: The isoparametric representation (The isoparametric representation, Ch_16).
Week 11: Isoparametric quadrilaterals (Isoparametric quadrilaterals, Ch_17).
Week 12: Shape functions (Shape functions, Ch_18).
Convergence criteria in finite element method (FEM Convergence Requirements, Ch_19).
Finite element analysis (FEA with ABAQUS and/or Salome-Meca).