Předmět MKP v mechanice (MKPME)

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Materiál	Typ	Datum	Počet stažení

Cíl

Studenti si rozšíří a prohloubí teoretické znalosti podstaty MKP a numerické postupy vedoucí k praktickému použití metody. Zejména bude prohloubena problematika řešení nelineárních úloh.

Osnova

Variational Methods. Principle of stationary potential energy. Problems having many degrees of freedom (DOF). Potentialenergy of an elastic body. The Rayleigh-Ritz method. Galerkin and other weighted residual methods (MWR). Examples:Uniform bar, Beam dynamics. Galerkin FEM in two dimensions. Bar and Beam Elements. Displacement-based elements. Shape functions. Stiffness matrix. Properties of stiffnessmatrices. Timoshenko beam element. Boundary conditions. Applied mechanical loads. Equilibrium equations. Stresses. FEM Concepts. Elements of arbitrary orientation – local and global matrices. Assembly of elements ( assemblyand structure node numbers ). Exploiting sparsity, numbering and sparsity. Solution of equations. Structural symmetry.Connecting dissimilar elements. Eccentric stiffeners. Rigid elements. Basic Elements. Preliminaries: Strain-displacement relations, Stress-strain relations. Interpolation and shapefunctions. Formulas for element matrices. Linear triangle ( constant-strain triangle CST ). Quadratic triangle( LST ). Bilinear rectangle ( Q4 ). Quadratic rectangle ( Q8, Q9 ). Rectangular solid elements. Choice of interpolation functions. Nature ofa finite element solution. Isoparametric Elements. Example- bar element. Bilinear quadrilateral ( Q4 ). Transformation. [B] matrix and stiffnessmatrix. Numerical integration and Gauss quadrature. One, two and three dimensions. Stiffness matrix integration.Static condensation. Stress calculation. Analysis of axisymmetric solids. Elasticity relations. Axisymmetric solid elements. Loads without axial symmetry. FEM in Structural Dynamics. Dynamic equation. Mass and damping matrices. Consistent and lumped (diagonal) massmatrix. Proportional damping, Eigenfrequencies (natural frequencies), eigenmodes (mode shapes) and solutions method.Reduction of the number of DOF. Response History. Modal methods. Harmonic response. Direct integration methods-explicit or implicit. Centraldifferences-stability conditions. Newmark family of methods. Heat Transfer and Selected Fluid Problems. Heat transfer: introduction. Finite element formulation. Transientthermal analysis – Modal method and direct integration. Acoustics and FE formulation. Boundary absorption. Fluid- structure interaction. Buckling. Geometric nonlinearity-Green strain. Energy considerations. Initial stress stiffness matrix ( geometricstiffness matrix ). Linear buckling. Imperfection. Nonlinear buckling. Nonlinearity. Newton-Raphson method. Arc-length method. Convergence criteria. Problems of gaps and contact.

Literatura

Cook R. D., Malkus D.S., Plesha M.E., Witt R.J. CONCEPTS AND APPLICATIONS OF FINITE ELEMENT ANALYSIS. 4th edition. J. Wiley & Sons, Inc. NY, 2002, p. 719, ISBN 0-471-35605-0 Zhi-Hua Zhong. Finite Element Procedures for Contact-Impact Problems. Oxford University Press, 1993, p. 371, ISBN 0-19 856383-3 REDDY, J.N., An Introduction Nonlinear Finite Element Analysis, Oxford University Press, 2004, p. 463, ISBN 0-19-852529-X WRIGGERS, P., Nichtlineare Finite-Element Metoden, Springer, 2005, p. 495, ISBN 3-540-67747BHATTI,M.A., Advanced Topics in Finite Element Analysis of Structures: with Mathematica and Matlab Computations, Wiley, 2006, p.590, ISBN-13 978-0-471-64807-9

Požadavky

Žádné

Garant

prof. Ing. Petr Horyl, CSc., dr.h.c.

Vyučující

prof. Ing. Petr Horyl, CSc., dr.h.c.