NONLINEAR DYNAMIC ANALYSIS OF PLATES SUBJECTED TO EXPLOSIVE LOADS

Abstract

BLAST LOADS HAVE BEEN INCREASINGLY STUDIED IN THE PAST DECADES, ESPECIALLY IN RECENT YEARS WITH THE GROWING INTEREST IN THE BEHAVIOR OF CIVIL STRUCTURES WHEN SUBJECTED TO THIS KIND OF PHENOMENON. UNTIL RECENTLY, THE NEGATIVE PHASE (SUCTION) OF THESE LOADS HAS BEEN DISREGARDED, BUT STUDIES CONCLUDED THAT THE EFFECT OF SUCTION IS CRUCIAL TO THE BEHAVIOR OF THE STRUCTURE, RESULTING IN LARGER DISPLACEMENTS THAN JUST CONSIDERING THE POSITIVE PHASE. IN THE CASE OF PLATES, SINCE DISPLACEMENTS CAN BE LARGER THAN USUAL, NONLINEARITY PLAYS AN IMPORTANT ROLE, AND THE MEMBRANE EFFECT SHOULD ALSO BE CONSIDERED. THIS WORK FOCUSES ON THE INFLUENCE OF NONLINEARITY IN PLATE STRUCTURES (MEMBRANE EFFECT) WHEN SUBJECTED TO BLAST LOADS CONSIDERING POSITIVE AND NEGATIVE PHASES. THE PROBLEM IS MODELED AS A SDOF (SINGLE DEGREE OF FREEDOM) APPLIED TO VON KARMAN'S THEORY OF LARGE DISPLACEMENTS. THE DEVELOPMENT OF THE NONLINEAR DYNAMIC DIFFERENTIAL EQUATION IS REVIEWED, CONSIDERING A SIMPLY SUPPORTED PLATE. EQUATIONS WERE ALSO DEVELOPED FOR THE CALCULATION OF BLAST LOAD PARAMETERS, AND IT IS CONSIDERED THAT THE CURVES FOR POSITIVE AND NEGATIVE PHASES ARE GIVEN BY THE FRIEDLANDER EQUATIONS AND CUBIC APPROXIMATION, RESPECTIVELY. THE SOLUTION OF THE NON-HOMOGENEOUS DIFFERENTIAL EQUATIONS IS BASED ON THE NUMERICAL METHOD OF RUNGE-KUTTA SINCE THERE ARE NO ANALYTICAL SCHEMES DUE TO NONLINEARITY. A REFERENCE EXAMPLE OF A SQUARE PLATE IS USED AS A BENCHMARK AND THEN PARAMETRIC STUDIES ARE CONDUCTED, IN WHICH THE INFLUENCE OF SCALED DISTANCE, MASS OF EXPLOSIVE, AND THE CONSIDERATION OR NOT OF THE NEGATIVE PHASE IS ANALYZED.