RESPONSE OF PARTIALLY CLOSED CELL EXPOSED TO CYCLIC LOAD by Tesfamicael Yohannes Teckle Contents 1.INTRODUCTION..............................................................................................................7 1.1 Objective and scope................................................................................................11 1.2 Contents..................................................................................................................11 2.PROBLEM FORMULATION.........................................................................................12 2.1 Description of the structural behaviour......................................................................12 2.2 Conditions and requiremets......................................................................................13 3.THEORETICAL BASIS...................................................................................................15 3.1 Part One.................................................................................................................15 3.1.1 Axis symmetry thin shelles..........................................................................15 3.1.2 Relationship between stresses and internal pressure.....................................16 3.2 Part Two................................................................................................................18 3.2.1 Relationship between strain and stress for compressible materials................18 3.2.2 Relationship of strain and displacement for incompressible materials............23 3.3 Part Three..............................................................................................................26 3.3.1 Transformation of Coordinates and Material constants for Axis-symmetric Models...............................................................................................................26 3.3.2 Discussion..................................................................................................27 4.MATHEMATICAL MODELING...................................................................................28 4.1 Calculation of forces................................................................................................28 4.2 Geometry................................................................................................................30 4.3 Desciption of elements.............................................................................................31 4.4 Shape functions for axis-symmetry solid elements.....................................................32 4.4.1 Shape functions for PLANE25 elements.....................................................32 4.4.2 Shape functions for PLANE83 elements.....................................................32 4.4.3 Mathematical formulation of B matrix..........................................................33 4.4.4 Boundry conditions....................................................................................35 4.4.5 Discussion..................................................................................................35 5.Results...............................................................................................................................41 5.1 Given informations..................................................................................................41 5.2 Stress analysis........................................................................................................42 5.3 Stresses and stress resultants..................................................................................43 5.4 Comparison of a 4-node and an 8-node element.....................................................45 5.5 Some methods and techniques in problem solving in ANSYS..................................51 5.5.1 Strain and stresses results for compressible material...................................53 5.5.2 Strain and stresses results for incompressible material.................................54 5.6 Tables and plots of resultant forces and moments....................................................56 6.Parametric studies and proposed simplified formula.......................................................70 6.1 Studies of pressure inside cell..................................................................................70 6.2 Proposed simplified formula....................................................................................71 6.6.1 Simplified formula for pressure inside cell....................................................72 6.6.2 Simplified formula for axial force distribution factor.....................................73 7.Verification of simplified formula.....................................................................................76 7.1 Verification of simplified formula.............................................................................76 7.2 Verification of formula for distribution factor of axial force.......................................77 8.Partially closed cell...........................................................................................................82 8.1 Dynamic analysis of partially closed cell..................................................................82 8.1.1 Volume flow due to reduction of cell body.................................................83 8.1.2 Volume flow in a pipe...............................................................................85 8.2 Relationship between Pi and volume flow Q..........................................................86 8.3 Correction factor ß for Pi.....................................................................................89 9.CONCLUSION................................................................................................................94 A.ANSYS command files and results.................................................................................97 A.1 Model program of cell part of platform without water............................................97 A.2 Model program of cell part of platform with water.................................................99 A.3 Calculation of sectional forces in ANSYS.............................................................99 A.4 Non dimensional parameteres..............................................................................101 A.5 Tables of deformations, strains and stresses.........................................................101 A.6 Tables strains and stresses...................................................................................107