NON-DETERMINISTIC LINEAR STATIC FINITE ELEMENT ANALYSIS: AN INTERVAL APPROACH

By DANIEL MARTINEZ

INTRODUCTION ALEATORY AND EPISTEMIC UNCERTAINTY APPROACHES FOR REPRESENTATION OF UNCERTAINTY PROBABILISTIC APPROACH FUZZY SET THEORY INTERVAL APPROACH UNCERTAINTIES AND ERRORS IN FINITE ELEMENT ANALYSIS MODEL UNCERTAINTY DISCRETIZATION ERROR PARAMETER UNCERTAINTY ROUNDING ERROR NONDETERMINISTIC FEA: AN INTERVAL APPROACH OBJECTIVE THESIS ORGANIZATION INTERVAL ARITHMETIC NOTATION INTERVAL NUMBER INTERVAL ARITHMETIC EXPRESSION DEPENDENCE PROBLEM INTERVAL VECTORS AND INTERVAL MATRICES LINEAR INTERVAL EQUATIONS INTERVAL COMPILERS AND PROGRAMMING ENVIRONMENTS C/C++ AND FORTRAN MATLAB MAPLE INTERVAL FEA: LITERATURE REVIEW DETERMINISTIC FEA INTERVAL FEA CLOSED-FORM SOLUTION COMBINATORIAL METHOD PERTURBATION METHOD SENSITIVITY ANALYSIS METHOD OPTIMIZATION METHOD MONTE CARLO SAMPLING METHOD NEED FOR ALTERNATIVE INTERVAL FEA INTERVAL FEA: DEVELOPMENT AND IMPLEMENTATION NA¨IVE INTERVAL ARITHMETIC FEA COMPUTATIONAL PROCEDURES INTERVAL ELEMENT STI?NESS MATRIX: FACTORIZATION OF INTERVAL PA- RAMETERS ASSEMBLY OF ELEMENTS: ELEMENT-BY-ELEMENT TECHNIQUE INTERVAL LOADS CONSTRAINTS: PENALTY METHOD AND LAGRANGE MULTIPLIERS SOLVING THE LINEAR INTERVAL EQUATION STRESSES AND ELEMENT NODAL FORCES CALCULATION FORMULATION USING THE LAGRANGE MULTIPLIERS FRAME ANALYSIS UNDER INTERVAL MATERIAL, CROSS-SECTIONAL PROP- ERTIES AND LOADS PLANE STRESS AND PLANE STRAIN ?NITE ELEMENTS WITH INTERVAL MA- TERIAL PROPERTY AND LOADS COMPUTER IMPLEMENTATION IMPLEMENTATION OF THE CONVENTIONAL INTERVAL FEA IMPLEMENTATION OF THE PRESENT INTERVAL FEA NUMERICAL EXAMPLES TRUSS STRUCTURE DETERMINISTIC ANALYSIS INTERVAL ANALYSIS BEAM STRUCTURE FRAME STRUCTURE CASE WITH ONLY LOAD UNCERTAINTY CASE WITH STI?NESS UNCERTAINTY AND LOAD UNCERTAINTY TRUSSES WITH A LARGE NUMBER OF INTERVAL VARIABLES SCALABILITY STUDY COMPUTATIONAL E?CIENCY STUDIES PLATE WITH QUARTER-CIRCLE CUTOUT CASE RECTANGULAR PLATE CONCLUSIONS AND FUTURE WORK CONCLUSIONS DIRECTIONS FOR FUTURE WORK IMPROVEMENT TO THE PRESENT INTERVAL FEA RELIABILITY ASSESSMENT USING THE INTERVAL FEA CONSIDERATION OF DISCRETIZATION ERROR REFERENCES