scholarly journals The recent stress state of Germany – results of a geomechanical–numerical 3D model

2021 ◽  
Vol 1 ◽  
pp. 163-164
Author(s):  
Steffen Ahlers ◽  
Andreas Henk ◽  
Tobias Hergert ◽  
Karsten Reiter ◽  
Birgit Müller ◽  
...  
Keyword(s):  
Stress State ◽  
Stress Field ◽  
Boundary Conditions ◽  
3D Model ◽  
Sedimentary Cover ◽  
Calibration Data ◽  
Orientation Data ◽  
Displacement Boundary ◽  
The Core ◽  
Continuous Description

Abstract. A decisive criterion for the selection and the long-term safety of a deep geological repository for high radioactive waste is the crustal stress state and its future changes. The basis of any prognosis is the recent crustal stress state, but the state of knowledge in Germany is quite low in this respect. There are stress orientation data provided by the World Stress Map (WSM, Heidbach et al., 2018) and stress magnitude data from a database (Morawietz et al., 2020) for Germany, both providing selective information on the recent stress field. However, these data are often incomplete, of low quality and spatially unevenly distributed. Therefore, a 3D continuous description is not possible with these data so far, at most for the orientation of the maximum horizontal stress (SHmax), but not for the most important magnitudes of the minimum (Shmin) and SHmax. In the course of the SpannEnD project, a geomechanical–numerical 3D model of Germany is created, with which a continuous description of the complete tensor of the recent stress field in Germany is possible. The model covers an area of 1250×1000 km2 from Poland in the east, to France in the west, from Italy in the south to Scandinavia in the north. The depth extent is 100 km. Even though the focus is primarily on Germany, the model area was chosen to be so wide to minimize boundary effects and for a simplified definition of the displacement boundary conditions, which are ideally oriented perpendicular or parallel to the orientation of SHmax. The model contains a total of 21 units: The upper part of the lithospheric mantle, the lower crust, four laterally overlapping units of the upper crust, and 14 stratigraphic units of the sedimentary cover. The stratigraphic subdivision of the sedimentary cover is only done in the core area of the model; because this area is the focus of our study, our calibration data are mainly from this region and well-resolved geometry data are available. Outside of the core area, the sediments are grouped into an undifferentiated unit. The units are parameterized with density and elastic material parameters (Poisson's ratio and Young's modulus). The model has a lateral resolution of 2.5×2.5 km2 and a vertical resolution of a maximum of 240 m; in total it includes 11.1 million hexahedral elements. The equilibrium of forces between body and surface forces is solved by finite element method. The model is calibrated with Shmin and SHmax magnitudes from the WSM and data from the stress magnitude database. First, an initial stress state is generated and in a second step displacement boundary conditions are defined at the model edges, which are adjusted until a best-fit to the calibration data is found. The results show good agreement with both the SHmax orientation data from the WSM and the magnitudes of the two principal horizontal stresses (Shmin and SHmax) from the magnitude database.

scholarly journals A numerical study of the impact perforation of sandwich panels with graded hollow sphere cores

2021 ◽  
Vol 13 (4) ◽  
pp. 168781402110094
Author(s):  
Ibrahim Elnasri ◽  
Han Zhao
Keyword(s):  
Boundary Conditions ◽  
Hollow Sphere ◽  
Sandwich Panel ◽  
Numerical Study ◽  
Sandwich Panels ◽  
Hopkinson Bar ◽  
Core Density ◽  
The Core ◽  
The Impact ◽  
Force Displacement

In this study, we numerically investigate the impact perforation of sandwich panels made of 0.8 mm 2024-T3 aluminum alloy skin sheets and graded polymeric hollow sphere cores with four different gradient profiles. A suitable numerical model was conducted using the LS-DYNA code, calibrated with an inverse perforation test, instrumented with a Hopkinson bar, and validated using experimental data from the literature. Moreover, the effects of quasi-static loading, landing rates, and boundary conditions on the perforation resistance of the studied graded core sandwich panels were discussed. The simulation results showed that the piercing force–displacement response of the graded core sandwich panels is affected by the core density gradient profiles. Besides, the energy absorption capability can be effectively enhanced by modifying the arrangement of the core layers with unclumping boundary conditions in the graded core sandwich panel, which is rather too hard to achieve with clumping boundary conditions.

scholarly journals Waves in Microstructured Conducting Sheath Helix Embedded Optical Guides with Chiral Nihility and Chiral Materials

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
N. Iqbal ◽  
M. A. Baqir ◽  
P. K. Choudhury
Keyword(s):  
Boundary Conditions ◽  
Flux Density ◽  
Energy Flux ◽  
Pitch Angle ◽  
Electromagnetic Waves ◽  
The Core ◽  
Dispersion Behavior ◽  
Chiral Materials ◽  
Energy Flux Density

The paper deals with the sustainment of electromagnetic waves in circularly cylindrical optical guide with chiral nihility and chiral materials in the core and the clad sections, respectively. A perfectly conducting tightly wound helix is introduced at the core-clad interface. The eigenvalue relation for such a complex optical microstructured guide is deduced by applying suitable boundary conditions at the core-clad interface, and the dispersion behavior is analyzed by varying the pitch angle of helix. The sustainment of energy flux density in such optical guides is estimated under various structural conditions, and the density patterns in core-clad sections are anatomized analytically.

Numerical Simulation of the Stress Field of Thick 7B04 Aluminum Alloy Board during Continuous Manufacture Procedure

2007 ◽  
Vol 127 ◽  
pp. 259-264
Author(s):  
Hong Yuan Fang ◽  
Cheng Iei Fan
Keyword(s):  
Numerical Simulation ◽  
Aluminum Alloy ◽  
Stress Concentration ◽  
Stress Field ◽  
Solution Treatment ◽  
Simulation Method ◽  
The Core ◽  
Manufacturing Procedure ◽  
Continuous Manufacture ◽  
Simulation Results

Numerical simulation method is employed in the article to analyze the stress field of thick 7B04 aluminum alloy board during manufacturing procedure of solution treatment, calendaring and stretching. The simulation results show that the surface of the board endures compressive stress while the core segment endures tensile stress, and the distribution of the stress is very inhomogeneous. The calendaring procedure helps to decrease the stress and redistribute the stress uniformly, but it also leads to stress concentration at the two ends of the board, which engenders bad influence on the subsequent processing. The board deforms plastically when being stretched, thus the stress decreases greatly and is redistributed uniformly.

scholarly journals Узагальнення моделі Голанда і Рейсснера на випадок осьової симетрії

2021 ◽  
pp. 12-19
Author(s):  
Костянтин Петрович Барахов
Keyword(s):  
Stress State ◽  
Analytical Solution ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Bessel Functions ◽  
Classical Model ◽  
Adhesive Bond ◽  
Radial Coordinate ◽  
Round Hole ◽  
Normal Stresses

The purpose of this work is to create a mathematical model of the stress state of overlapped circular axisymmetric adhesive joints and to build an appropriate analytical solution to the problem. To solve the problem, a simplified model of the adhesive bond of two overlapped plates is proposed. The simplification is that the movement of the layers depends only on the radial coordinate and does not depend on the angular one. The model is a generalization of the classical model of the connection of Holland and Reissner in the case of axial symmetry. The stresses are considered to be evenly distributed over the thickness of the layers, and the adhesive layer works only on the shift. These simplifications allowed us to obtain an analytical solution to the studied problem. The problem of the stress state of the adhesive bond of two plates is solved, one of which is weakened by a round hole, and the other is a round plate concentric with the hole. A load is applied to the plate weakened by a round hole. The discussed area is divided into three parts: the area of bonding, as well as areas inside and outside the bonding. In the field of bonding, the problem is reduced to third- and fourth-order differential equations concerning tangent and normal stresses, respectively, the solutions of which are constructed as linear combinations of Bessel functions of the first and second genera and modified Bessel functions of the first and second genera. Using the found tangential and normal stresses, we obtain linear inhomogeneous Euler differential equations concerning longitudinal and transverse displacements. The solution of the obtained equations is also constructed using Bessel functions. Outside the area of bonding, displacements are described by the equations of bending of round plates in the absence of shear forces. Boundary conditions are met exactly. The satisfaction of marginal conditions, as well as boundary conditions, leads to a system of linear equations concerning the unknown coefficients of the obtained solutions. The model problem is solved and the numerical results are compared with the results of calculations performed by using the finite element method. It is shown that the proposed model has sufficient accuracy for engineering problems and can be used to solve problems of the design of aerospace structures.

The Effects of Geometry and Static Boundary Conditions on Microvessel Outgrowth in a 3D Model of Angiogenesis

2010 ◽  
Author(s):  
Clayton J. Underwood ◽  
Laxminarayanan Krishnan ◽  
Lowell T. Edgar ◽  
Steve Maas ◽  
James B. Hoying ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Direct Relationship ◽  
3D Model ◽  
Mechanical Strain ◽  
Matrix Stiffness ◽  
Collagen Gels ◽  
3D Collagen ◽  
In Vitro Angiogenesis

We reported previously that, in addition to mechanical strain, a constrained boundary condition alone can alter the organization of microvessel outgrowth during in vitro angiogenesis [1]. After 6 days of culture in vitro, microvessels aligned parallel to the long axis of rectangular 3D collagen gels that had constrained edges on the ends. However, unconstrained cultures did not show any alignment of microvessels. The ability to direct microvessel outgrowth during angiogenesis has significant implications for engineering prevascularized grafts and tissues in vitro, therefore an understanding of this process is important. Since there is direct relationship between the ability of endothelial cells to contract 3D gels and matrix stiffness [2], we hypothesize that some constrained boundary conditions will increase the apparent matrix stiffness and in turn will limit gel contraction, prevent microvessel alignment, and reduce microvessel outgrowth. The objective of this study was to compare microvessel growth and alignment under several different static boundary conditions.

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