scholarly journals Elastic Foundation Displacement Approximations

2019 ◽  
Vol 14 (2) ◽  
pp. 125-135
Author(s):  
Vytautas Kargaudas ◽  
Nerijus Adamukaitis ◽  
Mykolas Žmuida ◽  
Algis Pakalnis ◽  
Saulius Zadlauskas
Keyword(s):  
Elastic Foundation ◽  
Elastic Half Space ◽  
Ideal Gas ◽  
Linear Elastic ◽  
Fair Representation ◽  
Soil Media ◽  
Spring System ◽  
Contact And Impact ◽  
Interaction Problem ◽  
Space Line

Interaction of an elastic foundation and structures like beams, plates and frames plays an essential role in investigating soil media in contact and impact mechanics. The solution to this interaction problem is complicated even the foundation is assumed as a linear elastic medium. E. Winkler suggested the fair representation of the foundation in 1867, and then, to bring it closer to reality, an interaction between the spring elements was introduced. In this paper, a relatively simple membrane-spring system is investigated, where an ideal gas is added under or above the membrane. In many cases, this constant pressure in the cavity modifies the solution and accuracy of the approximation is significantly increased. The cases of concentrated normal force and uniform distributed load are examined. The results of elastic half-space line displacements and the membrane displacements are presented.

On the Effects of Residual Stress in Microindentation Tests of Soft Tissue Structures

2004 ◽  
Vol 126 (2) ◽  
pp. 276-283 ◽  
Author(s):  
Evan A. Zamir ◽  
Larry A. Taber
Keyword(s):  
Residual Stress ◽  
Soft Tissue ◽  
Elastic Foundation ◽  
Elastic Properties ◽  
Material Properties ◽  
Soft Tissues ◽  
Elastic Half Space ◽  
Fe Model ◽  
Linear Elastic ◽  
Tissue Structures

Microindentation methods are commonly used to determine material properties of soft tissues at the cell or even sub-cellular level. In determining properties from force-displacement (FD) data, it is often assumed that the tissue is initially a stress-free, homogeneous, linear elastic half-space. Residual stress, however, can strongly influence such results. In this paper, we present a new microindentation method for determining both elastic properties and residual stress in soft tissues that, to a first approximation, can be regarded as a pre-stressed layer embedded in or adhered to an underlying relatively soft, elastic foundation. The effects of residual stress are shown using two linear elastic models that approximate specific biological structures. The first model is an axially loaded beam on a relatively soft, elastic foundation (i.e., stress-fiber embedded in cytoplasm), while the second is a radially loaded plate on a foundation (e.g., cell membrane or epithelium). To illustrate our method, we use a nonlinear finite element (FE) model and experimental FD and surface contour data to find elastic properties and residual stress in the early embryonic chick heart, which, in the region near the indenter tip, is approximated as an isotropic circular plate under tension on a foundation. It is shown that the deformation of the surface in a microindentation test can be used along with FD data to estimate material properties, as well as residual stress, in soft tissue structures that can be regarded as a plate under tension on an elastic foundation. This method may not be as useful, however, for structures that behave as a beam on a foundation.

NON-LINEAR VIBRATIONS OF A SLIGHTLY CURVED BEAM RESTING ON A NON-LINEAR ELASTIC FOUNDATION

1998 ◽  
Vol 212 (2) ◽  
pp. 295-309 ◽  
Author(s):  
H.R. Öz ◽  
M. Pakdemirli ◽  
E. Özkaya ◽  
M. Yilmaz
Keyword(s):  
Elastic Foundation ◽  
Curved Beam ◽  
Linear Elastic ◽  
Non Linear ◽  
Linear Vibrations

scholarly journals The influence of elastic deformations in high-strength structural materials on the hydrogen transport

2021 ◽  
Vol 225 ◽  
pp. 01010
Author(s):  
Polina Grigoreva ◽  
Elena Vilchevskaya ◽  
Vladimir Polyanskiy
Keyword(s):  
Chemical Potential ◽  
Potential Gradient ◽  
Elastic Solid ◽  
High Strength ◽  
Ideal Gas ◽  
Linear Elastic ◽  
Coupled Diffusion ◽  
Elastic Boundary ◽  
Linear Effects ◽  
Solid System

In this work, the diffusion equation for the gas-solid system is revised to describe the non-uniform distribution of hydrogen in steels. The first attempt to build a theoretical and general model and to describe the diffusion process as driven by a chemical potential gradient is made. A linear elastic solid body and ideal gas, diffusing into it, are considered. At this stage, we neglect any traps and non-linear effects. The coupled diffusion-elastic boundary problem is solved for the case of the cylinder under the tensile loads. The obtained results correspond to the experimental ones. Based on them, the assumptions about the correctness of the model and its further improvement are suggested.

scholarly journals REINFORCED CONCRETE COATING PLATES OF HIGHWAYS ON AN ELASTIC HALF-SPACE

2018 ◽  
Vol 14 (2) ◽  
pp. 149-157
Author(s):  
Slav D. Semeniuk ◽  
Roman V. Kumashov
Keyword(s):  
Reinforced Concrete ◽  
Static Analysis ◽  
Elastic Foundation ◽  
Strain State ◽  
Ritz Method ◽  
Elastic Half Space ◽  
Numerical Studies ◽  
Concrete Coating ◽  
Plate On Elastic Foundation ◽  
Made In

Static analysis of the stress-strain state of a plate on elastic foundation is made in two ways on the example of a reinforced concrete road plate 2PP30.18-30 series B3.503.1-1 intended for temporary roads. These plates are considered as a planar structure on an elastic foundation. The plates are calculated by the method of B.N. Zhemochkin using the Ritz method to determine plate deflections in the main system using the mathematical package «MathCad». Also the plates are calculated on the PC «LIRA». There are given the results of experimental and numerical studies in this article

Nonlinear vibration of Euler-Bernoulli beams resting on linear elastic foundation

2013 ◽  
Vol 15 (4) ◽  
pp. 439-449 ◽  
Author(s):  
Mehran Javanmard ◽  
Mahdi Bayat ◽  
Alireza Ardakani
Keyword(s):  
Nonlinear Vibration ◽  
Elastic Foundation ◽  
Linear Elastic
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