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Decomposition and clustering methods for the development of multiprocessor computer-based systems for studying the mechanics of three-dimensional composite structure. (English. Russian original) Zbl 0731.73098

Sov. Phys., Dokl. 35, No. 1, 34-36 (1990); translation from Dokl. Akad. Nauk SSSR 310, No. 3, 554-558 (1990).
In general, variational methods can be used effectively to solve problems in the mechanics of composite structures on the basis of shell models only if certain versions or others of the decomposition method and the structured approach to the organization of calculations are used, with the help of high-speed computer networks, parallel computers, or ultrahigh-throughput multiprocessors in a regime of network services. One version of the decomposition of composite structures was proposed e.g. by (*) V. N. Pajmushin [ibid. 273, 1083-1086 (1983; Zbl 0548.73009)]. It is based on a contact formulation of the problems of the mechanics of composite objects and makes it possible to develop efficient algorithms for solving them by direct methods adapted to systems based on ultrahigh- throughput dedicated desktop multiprocessors for the strength analysis of complex articles.
Let us examine the basic positions and distinguishing features of the use of this version of the decomposition method within the framework of variational methods for studying the strength, stability, and dynamic response of shell structures made of elements of arbitrary geometry. In accordance with (*), we select individual elements from the structure, and at the interfaces we introduce some unknown reactive interaction forces, which will be included in the number of independent functional arguments. Complexes of basic relations of the method are constructed on the basis of a Timoshenko kinematic model and an independent approximation of the transverse tangential stresses for the entire stac of layers in a shell element. For this purpose, the deformation of the composite structure is represented as consisting of two sequential steps and a variational formula of a mixed type which falls in the category of variational formulas of the Hamilton-Ostrogradskij-Reissner principle.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
74E30 Composite and mixture properties
49M27 Decomposition methods
74K15 Membranes

Citations:

Zbl 0548.73009