scholarly journals Influence of Boundary Conditions on Cracking of Sanxingdui Moon Bay City Wall

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Jin Qu ◽  
Jianlin Ma ◽  
Bai Yang
Keyword(s):  
Stress Distribution ◽  
Free Boundary ◽  
Tensile Stress ◽  
Boundary Conditions ◽  
Crack Spacing ◽  
Water Evaporation ◽  
Bottom Surface ◽  
City Wall ◽  
Fixed Boundary ◽  
Boundary Length

The Sanxingdui Moon Bay City Wall, in China, is built of pale-yellow sand and yellow-brown clay, and the yellow-brown layers are suffering severely. In order to discuss the desiccation cracks in a section of this wall, this paper conducts evaporation tests in laboratory and observes the variations in the characteristics of the boundary conditions of the bottom surface of the sample. The results show that the boundary conditions of the bottom surface of the sample consist of two free boundaries, two sliding boundaries, and one fixed boundary from the outside to the inside. During the drying process, the free boundary extends, but the fixed boundary shrinks; the sliding boundary also remains basically stable. We obtain the surface tensile stress distribution under different boundary conditions through stress analysis and deduce that the tensile stress distribution has a trapezoidal pattern. Moreover, we calculate the lower limit on the crack spacing of the sample using the energy method, and the double of the sum of the maximum sliding boundary length and the free boundary length is the upper limit to the crack spacing. Maintaining the stability of the soil moisture content of the site is the main factor in the protection of the earthen archaeological site under the humid conditions of the museum above the site. In order to reduce the water evaporation rate of the soil, the surface of the site should be coated by a protectant, the main determining features of which are permeability, tensile strength, and compatibility with the earthen site.

Investigation of the Complex Two Degrees of Freedom Systems for Force Limited Vibration

2004 ◽  
Author(s):  
Andre Cote ◽  
Ramin Sedaghati ◽  
Yvan Soucy
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Degrees Of Freedom ◽  
Simple Approach ◽  
Conservative Estimate ◽  
Two Degrees Of Freedom ◽  
Jet Propulsion ◽  
Fixed Boundary ◽  
Free Boundary Conditions ◽  
Force Data

Force Limited Vibration (FLV) Testing developed at Jet Propulsion Laboratory offers many opportunities to decrease the overtesting problem associated with traditional vibration testing. Among the force limited vibration methods, the complex two degrees of freedom system (TDFS) appears to be the most complete and versatile model which gives reasonably conservative force limits, and does not require extrapolation of interface force data for similar mounting structures and test articles. However there are some limitations to the complex TDFS model. The model is well adapted for nicely separated modes but issues regarding the closely space modes have not been fully addressed in the literature. Also, the complex TDFS model is based on free boundary conditions for the mounting structure, which appear to be natural for many cases such as spacecraft mounted on a launch vehicle. However this is not necessarily true for some other cases such as an electronic component mounted on a spacecraft antenna, which requires fixed boundary conditions. The main objective of this paper is to give greater insights into the complex TDFS method and propose methodologies to overcome its limitations. It is shown that a simple approach can be used to assure conservative estimate of the force limits in situations regarding closely spaced modes. It is also demonstrated that although the complex TDFS method is not perfectly adapted to fixed boundary conditions of the mounting structure, given certain precautions, it still provides good estimates of the force limits.

Identifying the Magnitude and Location of a Load on a Slender Beam Using a Strain Gage Based Force Transducer

2012 ◽  
Author(s):  
Edward T. Bednarz ◽  
W. D. Zhu ◽  
Scott A. Smith
Keyword(s):  
Boundary Conditions ◽  
Strain Gage ◽  
Cross Sections ◽  
Bending Moment ◽  
Force Transducer ◽  
Bottom Surface ◽  
Homogeneous Material ◽  
Variable Cross ◽  
Fixed Boundary ◽  
Unique Strain

A unique strain gage based method is developed to identify the magnitude and location of a load on a slender beam with non-homogeneous material, variable cross sections, and pinned, firm rest, soft rest, pinned-fixed, and fixed boundary conditions. Four uniaxial strain gages are mounted to the bottom surface of the beam, and the bending moment diagram of the beam can be constructed using measured strains on the beam. By combining individually scaled strain gage outputs, the magnitude and location of the load can be accurately identified. The strain gage based force transducer methodology is experimentally validated on prismatic beams with firm rest, soft rest, firm rest-fixed, and fixed boundary conditions, and a continuously tapered beam with rest boundary conditions. The force transducer methodology is independent of the boundary conditions of the beam and the error from strain gage drift due to uniform thermal expansion on a prismatic beam can cancel out.

Stress Distribution and Mass Transport Along Grain Boundaries During Steady-State Electromigration

1994 ◽  
Vol 338 ◽  
Author(s):  
M. Scherge ◽  
C. L. Bauer ◽  
W. W. Mullins
Keyword(s):  
Steady State ◽  
Stress Distribution ◽  
Grain Boundary ◽  
Boundary Conditions ◽  
Grain Boundaries ◽  
Driving Forces ◽  
Bottom Surface ◽  
Triple Junctions ◽  
Flux Divergence ◽  
Transient Time

ABSTRACTStress distribution and mass flux in the plane of each grain boundary within a polycrystalline thin-film conductor have been calculated during electromigration for zero flux divergence (steady state) and various boundary conditions. Steady state, representing a balance between the (applied) electric and (induced) stress driving forces, is assumed to develop after a short transient time. Boundary conditions at the intersection of grain boundaries with the top and bottom conductor surfaces (surface junctions) and with the conductor edges (edge junctions) are assumed to be of two types: open (flux passes freely) and closed (zero flux). Flux is assumed to pass freely at the intersection of grain boundaries with each other (triple Junctions). Several grain boundary configurations are considered, including individual boundaries, single triple junctions, and combinations thereof, assuming that bottom surface junctions (conductor/ substrate interface) are closed and that top surface junctions are either open (bare conductor) or closed (passivation layer). Results clearly show the formation of incipient holes and hillocks near the intersection of triple junctions and/or closed (blocked) edge junctions with open surface junctions.

scholarly journals Local Well-Posedness for Free Boundary Problem of Viscous Incompressible Magnetohydrodynamics

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 461
Author(s):  
Kenta Oishi ◽  
Yoshihiro Shibata
Keyword(s):  
Free Surface ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Stokes Equations ◽  
Mhd Flow ◽  
Transmission Conditions ◽  
Well Posedness ◽  
Anisotropic Space ◽  
Free Boundary Conditions ◽  
Incompressible Magnetohydrodynamics

In this paper, we consider the motion of incompressible magnetohydrodynamics (MHD) with resistivity in a domain bounded by a free surface. An electromagnetic field generated by some currents in an external domain keeps an MHD flow in a bounded domain. On the free surface, free boundary conditions for MHD flow and transmission conditions for electromagnetic fields are imposed. We proved the local well-posedness in the general setting of domains from a mathematical point of view. The solutions are obtained in an anisotropic space Hp1((0,T),Hq1)∩Lp((0,T),Hq3) for the velocity field and in an anisotropic space Hp1((0,T),Lq)∩Lp((0,T),Hq2) for the magnetic fields with 2<p<∞, N<q<∞ and 2/p+N/q<1. To prove our main result, we used the Lp-Lq maximal regularity theorem for the Stokes equations with free boundary conditions and for the magnetic field equations with transmission conditions, which have been obtained by Frolova and the second author.

Using the Multi-Parameter Fracture Mechanics for more Accurate Description of Stress/Displacement Crack Tip Fields

2013 ◽  
Vol 586 ◽  
pp. 237-240 ◽  
Author(s):  
Lucie Šestáková
Keyword(s):  
Stress Distribution ◽  
Fracture Mechanics ◽  
Boundary Conditions ◽  
Displacement Field ◽  
Singular Term ◽  
Crack Tip ◽  
Higher Order ◽  
Precise Description ◽  
Accurate Knowledge ◽  
Higher Order Terms

Most of fracture analyses often require an accurate knowledge of the stress/displacement field over the investigated body. However, this can be sometimes problematic when only one (singular) term of the Williams expansion is considered. Therefore, also other terms should be taken into account. Such an approach, referred to as multi-parameter fracture mechanics is used and investigated in this paper. Its importance for short/long cracks and the influence of different boundary conditions are studied. It has been found out that higher-order terms of the Williams expansion can contribute to more precise description of the stress distribution near the crack tip especially for long cracks. Unfortunately, the dependences obtained from the analyses presented are not unambiguous and it cannot be strictly derived how many of the higher-order terms are sufficient.

Stress Distribution in a Uniformly Rotating Equilateral Triangular Shaft

1955 ◽  
Vol 22 (2) ◽  
pp. 255-259
Author(s):  
H. T. Johnson
Keyword(s):  
Approximate Solution ◽  
Stress Distribution ◽  
Boundary Conditions ◽  
Plane Strain ◽  
Cross Section ◽  
Plane Stress ◽  
Biharmonic Equation ◽  
Approximate Solutions ◽  
Distribution Of Stresses ◽  
General Method

Abstract An approximate solution for the distribution of stresses in a rotating prismatic shaft, of triangular cross section, is presented in this paper. A general method is employed which may be applied in obtaining approximate solutions for the stress distribution for rotating prismatic shapes, for the cases of either generalized plane stress or plane strain. Polynomials are used which exactly satisfy the biharmonic equation and the symmetry conditions, and which approximately satisfy the boundary conditions.

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