The Optimization Of The Program For Cable-Membrane Structures' Analysis

In recent years, cable-membrane structures developed very quickly in China in terms of its number and range of application. The development of cable-membrane structures in and outside China and the present application state, the method for cable-membrane structures' design and the domestic and foreign software for the cable-membrane structures' analysis were introduced firstly in this paper. The demerits of the cable-membrane structures' analysis software MCSL were mainly talked about and the software was optimized accordingly. The availability and practicality of the optimized program were proved through the practical projects.The node numbering optimization module was added in the pre-processing section of the software MCSL. The mathematical theories and fundamental principles of four optimization algorithms for the numbering of mesh nodes were introduced. The algorithm programs were developed according to those optimization methods with Fortran90. Through some examples of cable-membrane structures, the optimization effects of various algorithms were compared and which algorithm was the best in different conditions were talked about. Meanwhile, the definition of the boundary condition and the method of adding boundary condition were revised.The LDL~T algorithm with band storage of the total stiffness matrix was adopted for solving stiffness equation instead of the inverse matrix algorithm with full storage which was used in the original program MCSL. The programs of assembling two-dimension total stiffness matrix with constant bandwidth and one-dimension total stiffness matrix with variable bandwidth with the element stiffness matrix of the cable and membrane elements. Basing on the band storage, the subroutine of the revised LDL~T algorithm, the subroutine of introducing the boundary condition with the method of multiplying large numbers and the subroutine of calculating support reaction were developed. The optimization effect of the LDL~T algorithm with band storage and other direct algorithms were compared in detail through some examples of cable-membrane structures.The total stiffness matrix of the cable-membrane structures was compressed into a one-dimension array only containing nonzero numbers. The subroutines of Gauss-Seidel and SORalgorithm basing on completely compressed storage of the total stiffness matrix were developed. The effect of the optimized Gauss-Seidel and SOR algorithm were compared with the original Gauss-Seidel and SOR algorithm whose stiffness matrix adopted full storage method.The mathematical theory of the PCG algorithm was introduced in detail. The nonzero numbers of the lower triangular part of the total stiffness matrix were stored in a one-dimension array. Basing on this storage method, the subroutines of J-CG algorithm, SSOR-CG algorithm and ICCG algorithm were developed with Fortran. These algorithms were applied to the solution of the stiffness equation of some cable-membrane structures and the optimization effects of various PCG algorithms were compared.The interface of the program MCSL and Sap2000 was built. The subroutine Saptransfer was developed with Fortran with the function of transforming the support reaction calculated by the program of cable-membrane structures' analysis into the node load applied on the structure which are written in the file $2K of Sap2000 to analyse the structures under the membrane. The load analysis of the cable-membrane structures of two practical projects were conducted with the optimized program. The results proved that the operating speed of the optimized program was quickened greatly and thus the optimized program had great value in the practical project.