Finite Element Method

Opublikowano: 06.04.2014 22:01

Subject name Finite Element Method
Type of subject               Specialization
Summary ECTS 2
Form of course 15h lecture, 15h laboratory
Lecturer                           Prof. Jerzy Osiński, Ph.D., D.Sc.; Jarosław Mańkowski, Ph.D.; Piotr Żach, Ph.D.
A brief outline:
Lecture
  • Finite Elements. Linear and quadratic approximation. Elements of flat triangular and quadrangular. Lagrange’s and Serendip’s polynomials. Spatial elements: trihedrons and cubes.
  • Basic equation. Stiffness matrix. One-dimensional finite elements: rods, strings, shafts - examples of calculations. Introduction displacements restrained.
  • Thermal calculations. The local coordinate systems. Trusses. Finite elements in systems with a turnover: beams, plates, shells.
  • Replacement concentrated load. Dynamical problems. The matrix of inertia. Methods of gathered and distributed masses. Calculation of their own frequency. Damping matrix, numerical integration of the equations of motion.
  • Nonlinear issues. Large deformations and displacements. Stability, elastic-plastic systems. Issues of thermal conductivity - steady and unsteady heat conduction. Thermo-mechanical issues.
  • Modeling of fluid mechanics problems - flows.
  • Practical rules for the use of MES systems. Pre- and postprocessors - accuracy. Symmetry and antisymmetry. Principles of similarities. Numbering.
  • Professional MES systems, related methods: Boundary Element Method.
Exercises
  • Analysis of movements in rod systems.
  • Determination of the components of stresses in the 2D plane.
  • Determination of the components of stresses in the 3D space.
  • Comparison of different mesh generators MES - assessment of the accuracy of obtained solutions.
  • Modeling contact issues.