DETERMINATION OF THE STRESS STATE OF A LAYER WITH A CYLINDRICAL CAVITY, LOCATED ON AN ELASTIC BASE AND GIVEN BOUNDARY CONDITIONS IN THE FORM OF DISPLACEMENTS

Author(s):  
V. Miroshnikov
Author(s):  
V. P. Revenko

The paper is devoted to the determination of the stress-deformed state of structurally heterogeneous bearing rectangular plates with a rectangular hole. The new analytical-numerical method (finite bodies) was used, to find the stress state of the plate with a hole. The method of finite bodies uses the conditional partition of the doubly-connected surface of the plate into simpler connected rectangular parts. On the lines of conditional contact, the conditions of ideal contact are taken into account, which ensure the equality of stresses, deformations and displacements. The perturbed stressed state, which is presented in the form of a series of functions, which is rapidly intercepted at a distance from the outline of the hole, is considered. A finite sum of solutions of a plane problem is used and the stress state of a perturbed state is given as a sum of a series for nonorthogonal functions. The components of vector of displacements and stresses are written. The determination of the coefficients of the sum of a series is based on the proposed method of satisfying all boundary conditions and the conditions of ideal contact to find the minimum of a generalized quadratic form. The numerical criterion for the convergence of the method is theoretically established. It is shown that the accuracy of satisfaction of boundary conditions and conditions of ideal contact is estimated by one number – the minimum of a generalized quadratic form.


2021 ◽  
Vol 11 (4) ◽  
pp. 1482
Author(s):  
Róbert Huňady ◽  
Pavol Lengvarský ◽  
Peter Pavelka ◽  
Adam Kaľavský ◽  
Jakub Mlotek

The paper deals with methods of equivalence of boundary conditions in finite element models that are based on finite element model updating technique. The proposed methods are based on the determination of the stiffness parameters in the section plate or region, where the boundary condition or the removed part of the model is replaced by the bushing connector. Two methods for determining its elastic properties are described. In the first case, the stiffness coefficients are determined by a series of static finite element analyses that are used to obtain the response of the removed part to the six basic types of loads. The second method is a combination of experimental and numerical approaches. The natural frequencies obtained by the measurement are used in finite element (FE) optimization, in which the response of the model is tuned by changing the stiffness coefficients of the bushing. Both methods provide a good estimate of the stiffness at the region where the model is replaced by an equivalent boundary condition. This increases the accuracy of the numerical model and also saves computational time and capacity due to element reduction.


2007 ◽  
Vol 24 (4) ◽  
pp. 1074 ◽  
Author(s):  
Norbert Kerwien ◽  
Thomas Schuster ◽  
Stephan Rafler ◽  
Wolfgang Osten ◽  
Michael Totzeck

The problem involves the determination of a biharmonic generalized plane-stress function satisfying certain boundary conditions. We expand the stress function in a series of non-orthogonal eigenfunctions. Each of these is expanded in a series of orthogonal functions which satisfy a certain fourth-order ordinary differential equation and the boundary conditions implied by the fact that the sides are stress-free. By this method the coefficients involved in the biharmonic stress function corresponding to any arbitrary combination of stress on the end can be obtained directly from two numerical matrices published here The method is illustrated by four examples which cast light on the application of St Venant’s principle to the strip. In a further paper by one of the authors, the method will be applied to the problem of the finite rectangle.


2020 ◽  
Vol 11 (2) ◽  
pp. 40-48
Author(s):  
Y. A Pronosin ◽  
M. D Kaygorodov ◽  
A. M Karaulov

Existing approaches which allow to reduce the settlement unevenness of buildings and structures have their own advantages and disadvantages. One of the promising methods for reducing shallow foundations the settlement unevenness, which are based on soft dust and clay soil, is the building or its part lowering. The effect is achieved by drilling vertical wellbores in the immediate proximity to the existing foundation from the side of the least settlement. At different times, domestic and foreign scientists were engaged in to the methods of horizontal and inclined drilling of wellbores, an important issue, when applying this technology, is the determination of drilling parameters, the influence of soil characteristics and the stress state of the soil around the well, on the roll reduction process. The article considers the influence of the soil strength characteristics on the stress state of the soil which are surrounding the wellbore, and the effect of the drilled wellbore radius on the formation of the critical state regions. The analytical solution is based on the use of the well-known relationship for determining the stress state around the well during pressiometric tests. From this ratio, tangential and radial stresses are determined, which are then checked according to the condition of the law of strength, thereby forming a picture of the stress state around the well. According to the presented methodology, the stress state of the soil around the wells was calculated, which allows calculating the zones of soil destruction and thereby determining the parameters of the wells and the geometry of their location depending on the goals, when regulating the sediment of slab foundations.


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