MODELS, ALGORITHMS AND SOLUTIONS OF PROBLEMS OF THERMOFORCE STUDY OF MULTI-LAYER STRUCTURES UNDER ACTION OF PENETRATING RADMIONS

V.N. Bakulin, V.A. Potopakhin
VANT. Ser.: Mat. Mod. Fiz. Proc 1997. Вып.1. С. 43.

      Novel multi-layer structures composed of reflecting, dispersing, absorbing, thermoinsulating and other layers of arbitrary structure have been recently proposed to protect people against injurious effect of penetrating radiations (highly intense fluxes of electrons; ions, neutral atoms), enhance strength, reduce mass and cost of vessels of NPP reactors, particle accelerators and other entities at action of intense thermoforce loads.
      When studying the thermoforce state (temperature fields and stressed-strained state parameters) and strength of such structures it is necessary to take into account features of poorly studied dynamic thjermoforce loading type which are concentrated energy fluxes (GEF); features of GEF interaction with structural material which results in essentially nonuniform energy release over the structure Volume leading to occurrence in it of highly intense local temperature, pressure fields rapidly varying with time, to variation in physical, mechanical, geometrical characteristics during the effect. The computation methods should therewith account the above layer properties and features, structural and other features of multi-layered vessels made of composite and conventional materials (inhomogeneity, anisotropy, transversal pliabilities, property variation with coordinates and time, etc.), multiple effects of CEF various in nature, variations in structure parameters from one effect to another:
      The approach developed by the authors is discussed which is based on derivation of non-linear dynamic 3-D and 2-D equations, including equations of bound thermal viscous elasticity, time-dependent heat conduction, etc. for layers imparted with all necessary properties at dynamic thermoforce loads, CEF and their solution using a combination of modified methods: the direct method, the discrete orthogonalization method, the Striklin method, the Khubolt finite-difference scheme. In this case it is possible to take into consideration the specificity of the CEF effects, multi-layered structure features, advantages of every method and obtain fairly simple computer algorithms.
      The advantages of the developed computational models, algorithms and computer programs for solving 3-D and 2-D non-linear dynamics problems are as follows:
      — no time step limitation is imposed;
      — the time step may be changed during problem solution and both static and dynamic problems can be solved using a single algorithm;
      — preliminary static loading and the possibility of repeated introduction of temperature fields, pressures, variations in structure parameters are taken into consideration.
      Employment of the developed software models considerably extends the range of solvable dynamic non-linear problems, including problems of coupled and uncoupled thermoelasticity, allows to refine the computed results arid formulate recommendations for designing, rhanufacture; operation of the structures under consideration.
      The developed experimental methods, developed and improved rigs and devices were used to conduct studies of the thermoforce state and strength of the above multi-layered structural elements under action of concentrated energy fluxes which confirmed the computed results.
      The work was carried out under the auspices of Russian Fundamental Research Foundation (project N-94-01- 01797a).

      The problem of porting application software developed for the third and fourth generation computers to a vector- pipeline super-computer was considered using the “Kompozit” application software package implementing the finite element method for strength and building mechanics problem solution.
      The objective of the application software porting is primarily to achieve a considerably, higher speed of computations as maximum possible performance of modern super-computers is considerably higher than that of previous generations. However, when executing most Fortran programs developed for serial computers, as a rule, it is impossible to achieve high performance on a super-computer due to incompatibility of the vector-pipeline architecture algorithms implemented in them which does not allow to use the advantages of the architecture in full measure.
      Many Fortran programs can be adapted to the vector-pipeline architecture with using the “vectorizing compiler” which effectively vectorizes simple and nested loops, as well as inner product type macroinstructions. Other Fortran programs can be adapted to the vector-pipeline architecture using loop rearrangement type local changes. Finally, there are Fortran programs whose adaptation to the vector-pipeline architecture requires more extensive transformations up to complete algorithm reconstruction.
      The window-oriented frontal method for solution of linear algebraic equation systems was discussed which combines the advantages of the frontal and band methods and allows to effectively vectorize the algebraic phases of the “Kompozit” package. Fortran-77 texts of the programs were given which implement the window-oriented frontal method. For vector computations vector subprograms in the “Elektronika SSBIS” super-computer system assembler language are developed which allow to enhance performance and reach super-vector performance at making the Kholesky frontal matrix factorization.