Modeling of stress states in intact layered rock massifs

Предложена структурная модель анизотропной среды для расчета напряженнодеформированного состояния в нетронутых массивах горных пород, которая учитывает ряд горнотехнических и горно-геологических факторов. Результаты аналитического решения позволили объяснить известные из практики натурных наблюдений факты (возможность превосходства горизонтальных напряжений над вертикальными, кусочно-линейный характер напряжений и т.д.), которые находились в противоречии с широко распространенными гипотезами о распределении напряжений в породных массивах. A structural model of an anisotropic medium is proposed for calculating the stressstrain state in intact rock massifs, which takes into account a number of mining and geological factors. The results of the analytical solution allowed us to explain the facts known from the practice of field observations (the possibility of the superiority of horizontal stresses over vertical ones, the piecewise linear nature of stresses, etc.), which were in contradiction with the widespread hypotheses about the distribution of stresses in rock massifs.

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Ratchet Boundary for Superimposed Biaxial Membrane Stress States

Volume 2: Computer Technology and Bolted Joints ◽

10.1115/pvp2018-85150 ◽

2018 ◽

Author(s):

Wolf Reinhardt

Keyword(s):

Thermal Expansion ◽

Thermal Stress ◽

Analytical Solution ◽

Pressure Vessels ◽

Stress Fields ◽

Design Codes ◽

Bending Stress ◽

Membrane Stress ◽

Asme Code ◽

Stress States

Thermal membrane and bending stress fields exist where the thermal expansion of pressure vessel components is constrained. When such stress fields interact with pressure stresses in a shell, ratcheting can occur below the ratchet boundary indicated by the Bree diagram that is implemented in the design Codes. The interaction of primary and thermal membrane stress fields with arbitrary biaxiality is not implemented presently in the thermal stress ratchet rules of the ASME Code, and is examined in this paper. An analytical solution for the ratchet boundary is derived based on a non-cyclic method that uses a generalized static shakedown theorem. The solutions for specific applications in pressure vessels are discussed, and a comparison with the interaction diagrams for specific cases that can be found in the literature is performed.

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An analytical solution to contaminant diffusion in semi-infinite clayey soils with piecewise linear adsorption

Chemosphere ◽

10.1016/j.chemosphere.2011.07.019 ◽

2011 ◽

Vol 85 (8) ◽

pp. 1248-1255 ◽

Cited By ~ 5

Author(s):

Haijian Xie ◽

Yunmin Chen ◽

Zhanghua Lou ◽

Liangtong Zhan ◽

Han Ke ◽

...

Keyword(s):

Analytical Solution ◽

Piecewise Linear ◽

Clayey Soils ◽

Contaminant Diffusion

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Study of Non-Linear Theory of Vertical Impact Damping System

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.66-68.119 ◽

2011 ◽

Vol 66-68 ◽

pp. 119-124

Author(s):

Jian Sheng Zhang

Keyword(s):

Transfer Function ◽

Analytical Solution ◽

Linear Theory ◽

Piecewise Linear ◽

Dynamical Response ◽

Compatibility Conditions ◽

Mechanics Model ◽

Theory Research ◽

Vertical Impact ◽

Impact Damping

A mechanics model of vertical impact damping system was founded based on the experimental device introduced in [1], and interrelated theory research was made on the mechanics model. The analytical solution of system dynamical response was gained using transfer function combining with the system’s neighboring boundary compatibility conditions in the fact of the piecewise linear characteristics of the system.

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Method of application of analytical solution of the piecewise linear approximation of magnetization curve on the example of calculation the peak-transformer parameters

Bulletin of NTU KhPI Series Problems of Electrical Machines and Apparatus Perfection The Theory and Practice ◽

10.20998/2079-3944.2019.2.10 ◽

2019 ◽

Vol 0 (2) ◽

pp. 52-56

Author(s):

Вячеслав Михайлович Боев ◽

Николай Яковлевич Петренко ◽

Виталий Игоревич Ревуцкий

Keyword(s):

Analytical Solution ◽

Linear Approximation ◽

Magnetization Curve ◽

Piecewise Linear ◽

Piecewise Linear Approximation

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Dynamic properties of piecewise linear systems with fractional time-delay feedback

Journal of Low Frequency Noise Vibration and Active Control ◽

10.1177/14613484211007633 ◽

2021 ◽

pp. 146134842110076

Author(s):

Jianchao Zhang ◽

Jun Wang ◽

Jiangchuan Niu ◽

Yufei Hu

Keyword(s):

Steady State ◽

Time Delay ◽

Analytical Solution ◽

Goodness Of Fit ◽

Numerical Solutions ◽

Dynamic Properties ◽

Piecewise Linear ◽

Steady State Solution ◽

State Solution ◽

Comparison Results

The forced vibration of a single-degree-of-freedom piecewise linear system containing fractional time-delay feedback was investigated. The approximate analytical solution of the system was obtained by employing an averaging method. A frequency response equation containing time delay was obtained by studying a steady-state solution. The stability conditions of the steady-state solution, the amplitude–frequency results, and the numerical solutions of the system under different time-delay parameters were compared. Comparison results indicated a favorable goodness of fit between the two parameters and revealed the correctness of the analytical solution. The effects of the time-delay and fractional parameters, piecewise stiffness, and piecewise gap on the principal resonance and bifurcation of the system were emphasized. Results showed that fractional time delay occurring in the form of equivalent linear dampness and stiffness under periodic variations in the system and influenced the vibration characteristic of the system. Moreover, piecewise stiffness and gap induced the nonlinear characteristic of the system under certain parameters.

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Analytical Solutions for Unsteady Groundwater Flow in an Unconfined Aquifer under Complex Boundary Conditions

Water ◽

10.3390/w12010075 ◽

2019 ◽

Vol 12 (1) ◽

pp. 75

Author(s):

Yawen Xin ◽

Zhifang Zhou ◽

Mingwei Li ◽

Chao Zhuang

Keyword(s):

Analytical Solution ◽

Groundwater Flow ◽

Piecewise Linear ◽

Unconfined Aquifer ◽

Piecewise Linear Approximation ◽

Level Fluctuation ◽

Level Variation ◽

Groundwater Dynamics ◽

River Level ◽

Complex Boundary

The response laws of groundwater dynamics on the riverbank to river level variations are highly dependent on the river level fluctuation process. Analytical solutions are widely used to infer the groundwater flow behavior. In analytical calculations, the river level variation is usually generalized as instantaneous uplift or stepped, and then the analytical solution of the unsteady groundwater flow in the aquifer is derived. However, the river level generally presents a complex, non-linear, continuous change, which is different from the commonly used assumptions in groundwater theoretical calculations. In this article, we propose a piecewise-linear approximation to describe the river level fluctuation. Based on the conceptual model of the riverbank aquifer system, an analytical solution of unsteady groundwater flow in an unconfined aquifer under complex boundary conditions is derived. Taking the Xiluodu Hydropower Station as an example, firstly, the monitoring data of the river level during the period of non-impoundment in the study area are used to predict the groundwater dynamics with piecewise-linear and piecewise-constant step approximations, respectively, and the long-term observation data are used to verify the calculation accuracy for the different mathematical models mentioned above. During the reservoir impoundment period, the piecewise-linear approximation is applied to represent the reservoir water level variation, and to predict the groundwater dynamics of the reservoir bank.

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Analytical nonlinear flutter and sensitivity analysis of aircraft wings subjected to a transverse follower force

Proceedings of the Institution of Mechanical Engineers Part G Journal of Aerospace Engineering ◽

10.1177/0954410017754171 ◽

2018 ◽

Vol 233 (4) ◽

pp. 1503-1515 ◽

Cited By ~ 3

Author(s):

E Zafari ◽

MM Jalili ◽

A Mazidi

Keyword(s):

Sensitivity Analysis ◽

Analytical Solution ◽

Structural Model ◽

Multiple Scales ◽

Unit Length ◽

Time History ◽

Follower Force ◽

Design Parameters ◽

Wing Chord ◽

Flutter Margin

In the present study, the nonlinear aeroelastic and sensitivity analysis of high aspect ratio wings subjected to a transverse follower force are discussed. A nonlinear structural model of wings is extracted and coupled with an incompressible unsteady aerodynamic model. The governing equations of motions are obtained via Hamilton’s principle and Galerkin method. Utilizing the method of multiple-scales, analytical approximate flutter response of the system is obtained. For validation, the analytical solution is compared with numerical solution and good agreement is observed. The time history of the tip displacement and tip twist solution are plotted for different airspeeds. Effects of follower force and its spanwise location and also the wing geometric characteristics on the flutter margin are discussed. Moreover, flutter margin sensitivity to different design parameters is analyzed. Results indicate that increasing the wing chord makes the system unstable. Furthermore, according to the analytical solution, effects of the wing chord and mass per unit length on the flutter margins are more important than the other system parameters.

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