# CTW - PT (EN)

 Course language English Course description Based on conservation laws for mass, momentum and energy, several differential equations, relevant to mechanical engineering, are derived. These are equations for a mass-spring system, the convection-diffusion equation, the wave eqution, the Laplace equation, the Poisson equation, the Helmholtz equation and the bi-harmonic equation. The equations are subdivided in hyperbolic, parabolic and elliptic equations.Thereafter, discretization methods are introduced. Spatial discretization is handled by finite difference, finite volume and finite element methods. Explicit and implicit methods are used for time discretization. The consistency, convergence and stability of the different methods will be evaluated.For linear static applications detailed attention is given to the assembly of a set of equations, the application of boundary conditions and constraints and the efficient solution of a model, using either direct or iterative solvers, submodelling and substructuring. The accuracy of results will be assessed using error estimators. Plate and shell elements are introduced. Elements will be scrutinised for locking phenomena like shear, volume and membrane locking. For dynamic analysis, eigen value analysis with subspace and Lanczos iterations are treated, statical reduction techniques, modal solution methods and direct time integration. For geometrically nonlinear situations incremental-iterative solution methods are introduced as the Newton-Raphson method, arclength control and line search techniques. Finally linear stability analysis is treated. GOAL: Insight in numerical methods for solid and fluid mechanics and application in dynamical and/or nonlinear situations. Participating progr. Mechanical Engineering (ME) Phase MSemester S1Biomedical Engineering (BME) Phase MSemester S1 Teaching methods Lecture Contact hours p/w 4 Assessment Partial written exam, practical assignment and final verbal exam Prior knowledge Obligatory: 115413 Introduction to fluid dynamics 115711 Introduction to the finite element methodNecessary: introductions to linear algebra, mechanics of materials, fluid mechanicsDesired: introduction to finite element analysis Credits 5.0 EC Inquiries bij de docenten Contact person dr.ir. A.H. van den Boogaard Teaching staff Course material Diktaat: Numerical Methods in Mechanical Engineering, Part I: Continuum Mechanics, Related Equations and Discretization Methods, R. Hagmeijer Boek: Concepts and Applications of Finite Element Analysis, R.D. Cook, D.S. Malkus, M.E. Plesha, R.J. Witt, 4th ed., ISBN 0-471-35605-0 Extra information Students that have not completed Finite Elements in the Mechanical Engineering and/or have to finish Numerical Fluid mechanics, can contact the lecturer. URL http://teletop.utwente.nl