MATLAB Codes for Finite Element Analysis

Cover -- Contents -- 1 Short introduction to MATLAB -- 1.1 Introduction -- 1.2 Matrices -- 1.3 Operating with matrices -- 1.4 Statements -- 1.5 Matrix functions -- 1.6 Conditionals, if and switch -- 1.7 Loops: for and while -- 1.8 Relations -- 1.9 Scalar functions -- 1.10 Vector functions -- 1.11 Matrix functions -- 1.12 Submatrix -- 1.13 Logical indexing -- 1.14 M-files, scripts and functions -- 1.15 Graphics -- 1.15.1 2D plots -- 1.15.2 3D plots -- 1.16 Linear algebra -- 2 Discrete systems -- 2.1 Introduction -- 2.2 Springs and bars -- 2.3 Equilibrium at nodes -- 2.4 Some basic steps -- 2.5 First problem and first MATLAB code -- 2.6 New code using MATLAB structures -- 3 Analysis of bars -- 3.1 A bar element -- 3.2 Numerical integration -- 3.3 An example of isoparametric bar -- 3.4 Problem 2, using MATLAB struct -- 3.5 Problem 3 -- 4 Analysis of 2D trusses -- 4.1 Introduction -- 4.2 2D trusses -- 4.3 Stiffness matrix -- 4.4 Stresses at the element -- 4.5 First 2D truss problem -- 4.6 A second truss problem -- 4.7 An example of 2D truss with spring -- 5 Trusses in 3D space -- 5.1 Basic formulation -- 5.2 A 3D truss problem -- 5.3 A second 3D truss example -- 6 Bernoulli beams -- 6.1 Introduction -- 6.2 Bernoulli beam problem -- 6.3 Bernoulli beam with spring -- 7 2D frames -- 7.1 Introduction -- 7.2 An example of 2D frame -- 7.3 Another example of 2D frame -- 8 Analysis of 3D frames -- 8.1 Introduction -- 8.2 Stiffness matrix and vector of equivalent nodal forces -- 8.3 First 3D frame example -- 8.4 Second 3D frame example -- 9 Analysis of grids -- 9.1 Introduction -- 9.2 A first grid example -- 9.3 A second grid example -- 10 Analysis of Timoshenko beams -- 10.1 Introduction -- 10.2 Formulation for static analysis -- 10.3 Free vibrations of Timoshenko beams -- 10.4 Buckling analysis of Timoshenko beams -- 11 Plane stress -- 11.1 Introduction -- 11.2 Displacements, strains and stresses -- 11.3 Boundary conditions -- 11.4 Potential energy -- 11.5 Finite element discretization -- 11.6 Interpolation of displacements -- 11.7 Element energy -- 11.8 Quadrilateral element Q4 -- 11.9 Example: plate in traction -- 11.10 Example: beam in bending -- 12 Analysis of Mindlin plates -- 12.1 Introduction -- 12.2 The Mindlin plate theory -- 12.2.1 Strains -- 12.2.2 Stresses -- 12.3 Finite element discretization -- 12.4 Example: a square Mindlin plate in bending -- 12.5 Free vibrations of Mindlin plates -- 12.6 Buckling analysis of Mindlin plates -- 13 Laminated plates -- 13.1 Introduction -- 13.2 Displacement field -- 13.3 Strains -- 13.4 Strain-displacement matrix B -- 13.5 Stresses -- 13.6 Stiffness matrix -- 13.7 Numerical example -- 13.8 Free vibrations of laminated plates -- References -- Index.