BOUNDARY ELEMENT METHODS IN SOLID MECHANICS
CONTENTS SHORT INTRODUCTION TO MATLAB INTRODUCTION MATRICES OPERATING WITH MATRICES STATEMENTS MATRIX FUNCTIONS CONDITIONALS, IF AND SWITCH LOOPS: FOR AND WHILE RELATIONS SCALAR FUNCTIONS VECTOR FUNCTIONS SUBMATRIX LOGICAL INDEXING M-?LES, SCRIPTS AND FUNCTIONS GRAPHICS 1 15 1 2D PLOTS 1 15 2 3D PLOTS LINEAR ALGEBRA DISCRETE SYSTEMS SPRINGS AND BARS EQUILIBRIUM AT NODES SOME BASIC STEPS FIRST PROBLEM AND ?RST MATLAB CODE NEW CODE USING MATLAB STRUCTURES ANALYSIS OF BARS A BAR ELEMENT NUMERICAL INTEGRATION AN EXAMPLE OF ISOPARAMETRIC BAR PROBLEM 2, USING MATLAB STRUCT PROBLEM 3 ANALYSIS OF 2D TRUSSES 2D TRUSSES STI?NESS MATRIX STRESSES AT THE ELEMENT FIRST 2D TRUSS PROBLEM A SECOND TRUSS PROBLEM AN EXAMPLE OF 2D TRUSS WITH SPRING TRUSSES IN 3D SPACE BASIC FORMULATION A 3D TRUSS PROBLEM A SECOND 3D TRUSS EXAMPLE BERNOULLI BEAMS BERNOULLI BEAM PROBLEM BERNOULLI BEAM WITH SPRING 2D FRAMES AN EXAMPLE OF 2D FRAME ANOTHER EXAMPLE OF 2D FRAME ANALYSIS OF 3D FRAMES STI?NESS MATRIX AND VECTOR OF EQUIVALENT NODAL FORCES FIRST 3D FRAME EXAMPLE SECOND 3D FRAME EXAMPLE ANALYSIS OF GRIDS A ?RST GRID EXAMPLE A SECOND GRID EXAMPLE ANALYSIS OF TIMOSHENKO BEAMS FORMULATION FOR STATIC ANALYSIS FREE VIBRATIONS OF TIMOSHENKO BEAMS BUCKLING ANALYSIS OF TIMOSHENKO BEAMS PLANE STRESS DISPLACEMENTS, STRAINS AND STRESSES BOUNDARY CONDITIONS POTENTIAL ENERGY FINITE ELEMENT DISCRETIZATION INTERPOLATION OF DISPLACEMENTS ELEMENT ENERGY QUADRILATERAL ELEMENT Q4 EXAMPLE: PLATE IN TRACTION 11 10 EXAMPLE: BEAM IN BENDING ANALYSIS OF MINDLIN PLATES THE MINDLIN PLATE THEORY 12 2 1 STRAINS 12 2 2 STRESSES EXAMPLE: A SQUARE MINDLIN PLATE IN BENDING FREE VIBRATIONS OF MINDLIN PLATES BUCKLING ANALYSIS OF MINDLIN PLATES LAMINATED PLATES DISPLACEMENT ?ELD STRAINS STRAIN-DISPLACEMENT MATRIX B STRESSES NUMERICAL EXAMPLE FREE VIBRATIONS OF LAMINATED PLATES REFERENCES