Vol.1, No 8, 2001 pp. 947 - 954
UDC 621.7:539.377 621.7:539.388.2
CALCULATION OF DESTRUCTION MECHANICS
PARAMETERS AND TEMPERATURE
OF DISSIPATIVE HEATING BY SINGULAR
THREE-DIMENSIONAL FINITE ELEMENTS IN CONDITIONS
OF NONLINEAR VISCOELASTIC DEFORMATION
V. V. Kirichevsky1, V.A.Tolok1,
S.N. Grebenyuk1, R.V. Kirichevsky2
1Zaporozhye State University, Faculty
of Mathematics and economic cybernetics, Zhukovsky str., 66, GSP-41, Zaporozhye,
Ukraine
2Lugansky State Agrarian University,
Lugansk-8, LSAU, Ukraine
Abstract. For sizing of constructions from weak compressible materials
difficulties are appeared, arising with use of a traditional finite element
method. That difficulties are connected with properties of rigidity matrix,
the moment scheme of finite elements with threefold approximation function
of displacement fields, component of deformations and function of volume
change is developed [1].
One of the most widespread defects is the crack. From analytical solutions
it is known, that about top of a crack the distribution of stresses and
deformations has a feature , where r - distance from a point of a
construction up to top of a crack. To calculate constructions with a crack
it's necessary to simulate that feature of deformations and stresses using
special finite elements. As special finite elements are applicable singular
triangular prismatic finite elements and singular parallelepiped finite
elements [2,3].
The power approach of determination of factors of stress intensity
for designs from viscoelastic material is submitted in the work. The component
of J-integral and factors of stress intensity are meanings by the method
of equivalent volumetric integration. The method of definition of
dissipative temperature and warm sources is offered with the decision
of a heat conduction task in nonlinear statement. The algorithm of definition
of warm sources is developed with the decision of the task by step-by-step
iterative methods. For solution of nonlinear problems we shall take advantage
of a modified method of Newton - Cantorovich in a combination to a method
of an integration on the parameter of a load, or on the parameter of a
strain with verification of the equations of balance.
The given method is realized on PC IBM within the framework of the
computer complex 'MIRELA', intended for the decision of tasks of the mechanics
of the deformed rigid body and mechanics of destruction elastomer and composite
constructions. The factors of stress intensity of the trapezoid shock-absorber
with the crack are determined with the given complex. The solution of a
problem in nonlinear setting conducts to change not only a value of factors
of stress intensity, but a also character of their distribution.
The influence of the crack on distribution of dissipative temperature
is considered. It is possible to make a conclusion of the analysis of obtained
results , that the availability of a crack and the account of nonlinearity
has an effect for change of character of distribution and value of temperature
of dissipative heating.
PRORAČUN PARAMETARA MEHANIKE LOMA I TEMPERATURE
DISIPATIVNOG ZAGREVANJA
POMOĆU SINGULARNIH TRODIMENZIONIH
KONAČNIH ELEMENATA U USLOVIMA NELINEARNE VISOKOELASTIČNE
DEFORMACIJE
Pri proračunu konstrukcija od slabo kompresibilnih materijala pojavljuju
se teškoće pri primeni tradicionalne metode konačnih elemenata. Teškoće
su povezane sa svojstvima matrice krutosti, isto tako momentna šema konačnih
elemenata sa trostrukom aproksimacijom funkcije polja deformacije, komponente
deformacija i funkcija promene zapremine su izvedene.
Takođe je ponuđen i metod za određivanje disipativne temperature i
toplih izvora pri rešavanju problema toplotne kondukcije sa nelinearnim
graničnim uslovima. Za rešavanje nelinearnih problema primenjen je modifikovani
metod Newton-Cantorovich-a.
