METHOD FOR DETERMINING REDUCTION FACTOR OF BEARING CAPACITY OF AXIAL LOAD CYLINDRICAL SHELL STRUCTURE

摘要

A method for determining a reduction factor of a bearing capacity of an axial load cylindrical shell structure relates to stability checking of main bearing strength thin-walled members of aerospace and architectural structures. Different from experiment experience-based conventional defect sensitivity evaluating method represented by NASA SP-8007, a depression defect is introduced in a manner of applying a radial disturbance load. First, an influence rule of a depression defect amplitude of a single point to an axial load bearing capacity is analyzed by using numerical values, so as to determine a load amplitude range; then, defect sensitivity analysis is performed on depression defects of multiple points; then, experiment design sampling is performed by using load amplitude values and load position distribution as design variables; and finally, based on optimizing technologies such as an enumeration method, a genetic algorithm and a surrogate model, the most disadvantageous disturbance load of the multiple points that limits the defect amplitude is searched for, and a reduction factor of the bearing capacity of the axial load cylindrical shell structure is determined, so as to establish a more physical method for evaluating the defect sensitivity and the bearing performance of the axial load cylindrical shell structure.

主权项

1. A method for determining a knockdown factor of load-carrying capacity of a cylindrical shell subjected to axial compression, the method comprising:
a) introducing single dimple imperfection to a perfect cylindrical shell by applying radial perturbation load to the perfect cylindrical shell, calculating load-carrying capacities of the cylindrical shell subjected to axial compression with different amplitudes of dimple imperfection through finite element analysis, performing imperfection sensitivity analysis to obtain a relationship between radial perturbation load and a sensitivity to load-carrying capacity of structure, and determining a rational perturbation load range, where a considered maximum imperfection amplitude corresponding to a maximum perturbation load Nmax is determined by fabrication quality and detection tolerance; b) performing imperfection sensitivity analysis using a combined dimple shape after introducing the dimple imperfections following the operations in 1), where a vertex of a regular polygon acts as the load position of the radial perturbation load; for n dimple imperfections, defining a distance between a circumcenter and a vertex of a n-sided regular polygon as l, varying the distance l from zero, calculating corresponding buckling loads, and drawing a curve representing the relationship between the buckling load and the distance l; defining the distance corresponding to a minimum buckling load as an effective distance le, Sa and Sc being distances of two adjacent load positions in the axial and circumferential directions, respectively, na and nc being the numbers of load positions in the axial and circumferential directions, respectively, calculation formulas thereof being as follows:Sa=l+0.5l=1.5lSc=3l/2na=LSa-1=2L3l-1nc=2πRSc=4πR3lwhere, L is an axial height of the cylindrical shell, R is a radius of the cylindrical shell;to facilitate calculation, herein defining l as le, and after determining na and nc, assigning a position number to each load position, the position number starting from zero degree at the bottom of the cylindrical shell, successively increasing from the bottom to the top along the axial direction, and then successively increasing along the circumferential direction; setting the amplitude of radial of perturbation load N as a design variable, Nmax as an upper bound, zero or a small empirical value as a lower bound; considering a calculation efficiency, a suggested number of dimple imperfections being 3;
c) in design of experiment, the amplitude of radial perturbation load N and the numbers na, nc of the load positions of the dimple imperfections as variables; and d) determining the combination of the perturbation loads that represents the realistic worst imperfection for the cylindrical shell using optimization technologies selected from an enumeration method, genetic algorithm and surrogate model; the optimization objective is to minimize the buckling load of the cylindrical shell with the combined dimple imperfection, and the optimization formulation is expressed as follows:
Design Variable: X=[N,N1,N2, . . . ,Nn]Objective Function: Pcr Subject to: Xil≦Xi≦Xiu, i=1,2, . . . ,n+1where, Nn is the position number of the nth perturbation load, Pcr is a buckling load of the cylindrical shell subjected to axial compression, Xil is an upper bound of ith variable, and Xiu is a lower bound of ith variable;after the optimization, a knockdown factor (KDF) is calculated via a formula:KDF=PcrimPcrpewhere, Pcrim is a buckling load of axially compressed cylindrical shell with the combination of the perturbation loads that represents the realistic worst imperfection, and Pcrpe is a buckling load of the perfect axially-compressed cylindrical shell.