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Computational and Informational Technologies for Research, Engineering and Education

CIT-2004

Alma-Ata, Kazakhstan, October, 6 - 10, 2004

Abstracts


Variational-difference method of the numerical analysis

Barashkov V.N.

Scientific Research Institute of Applied Mathematics and Mechanics (Tomsk)

The methodses of the calculation stress-strained state (SSS) hurlled assemblies in two-dimensional axis-symmetrical and spatial production with use quasistatics approach, which motivation is presented in [1] are stated in work. For work with appearing according to Dalamber’s principle [2] fictitious mass power notion of the factor of the overloading (or simply overloading N), which is defined by attitude of the speedup of the body a at present to speedup of power to gravity g: N = a/g is entered. Got at system of the loads is self-balanced, but from consideration constant forming axial displacement element assemblies is excluded.

The process of the speediest throwing by high intensity acting loads on hurlled elements and auxiliary device - a trays and leading device (LD), by means of which is realized runaway of the assembly is characterized. Increasing to velocities of the throwing element brings about increase acting on assembly of the loads, undesirable level deformation and voltages and destruction, both most assemblies, and launcher. The experimental studies composition schemes like design under their designing and master are necessary and obligatory stage. Considering greater temporary, financial and economic expenses when undertaking of these work, natural is a longing designer and constructor to use the mathematical methods mechanical engineers deformed hard body for modeling SSS element of the assembly when throwing for the reason reductions of the experimental test. So presence of the methodses of the analysis SSS like design, founded on modern numerical method are necessary under their designing. The analysis elastoplastic SSS of the hurlled assembly by variational-difference method (VDM), realizing extreme variational Lagrange’s principle for functional of the full potential energy of the system «body-load» method of the final differences is conducted. The equations of the balance and steady-state border conditions serves the Eilera’s equations for functional of the energy. So at decision of the problem elastoplasticty in variational production there is no need to beforehand satisfy the border condition in voltages. VDM reduces the problem to finding the extremum to functions many variable - a component of the vector of the displacement in nodes certainly-difference of the net, inflicted corresponding to image on under investigation body. When sampling functional energy for derived so named natural aproximations are used.

For decision elastoplastic problems deformational theory placticity. The geometrical correlations in the manner of Cauchy’s equations is used. In general event functional energy is an íåêâàäðàòè÷íûì and decision physically nonlinear problem is reduced to consequent minimization square-law functionales with elaborated in each approach parameter non-linear. The realization of the system of the linear algebraic equations of the big order for sought displacement, to which brings use the necessary condition of the extremum of net analogue functional energy, by direct and iterative methods is conducted.

At decision two-dimensional axis-symmetrical problems numerical experiment on discovery the most profitable level with standpoint of the voltages and deforming the variant to designs of the tray for throwing the pivotal element by change parameter to its geometry under fixed to length was marketed. The questions rational of strength designing axis-symmetrical assemblies for the reason reduction of the mass LD and increasing to velocities of the throwing the element were considered.

The numerical analysis three-dimensional deformation three alike sectors LD type «spool» when throwing heavy pivot the zone of the comb (join sector and pivot), as the most laden local area sector, where is noted significant unevenness of the sharing the voltages and deformation on its length, capable to bring about destruction of the assembly has revealled. For voltage level reduction and deformation is offered and marketed several technical decisions that has allowed vastly to reduce the values a parameter SSS on the comb before importances, allowing guarantee wholeness a sector LD and whole assemblies. The called on estimations of the influence of the temperature on SSS sector LD for several warm-up modes significant some parameter SSS have revealled, though integral values, characterizing deformation sector, practically did not change were increased.

LITERATURE

1 Barashkov V.N. The numerical analysis deformation hurlled tray // Modern methods of the designing and master racket-artillery arms: Collection reports II scientific conference Volga’s regional centre Russia Academy Racket-Artillery Science (RARAS), Sarov, 29 may–01 june 2001 year. – Sarov: Publishing house Russia Federal Nucleur Centre–All-Russia Scientific-Research Institute of Experiment Physics (RFNC-ARSRIEP). – 2003. – Pp. 71–78.

2. Boyarshinov S.V. Bases building mechanical engineers machines: Educational text-book. – M.: Mechanical engineering, 1973. – 456 p.

Note. Abstracts are published in author's edition



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