Interaction analysis between multiple non-circular lined tunnels and layered media

Authors: Ye, Zi Kun ^{a, b, c}, Ai, Zhi Yong ^{c, ⁎}, Bao, Xiaohua ^{a, b}, Chen, Xiangsheng ^{a, b}

Source: In Engineering Analysis with Boundary Elements December 2025 181

Dynamic responses and failure characteristics of surrounding rock in a deep-buried tunnel with an arbitrary cross-section subjected to blasting P-wave

Authors: Mei, Wanquan ^a, Pan, Pengzhi ^{a, ⁎}, Wang, Zhaofeng ^a, Xie, Yi ^{a, b}, Feng, Yujie ^a, Chi, Fudong ^c

Source: In Computers and Geotechnics October 2025 186

Analytical Solutions of Elastic Complex Variables for Tunnels with Complicated Shapes Under Geostress Field

Authors: Fan, Tianrui^{Aff1, Aff2, IDs0060302303753x_cor1}, Wang, Jiachen^{Aff1, Aff2}, Wang, Zhaohui^{Aff1, Aff2}

Source: Rock Mechanics and Rock Engineering. :1-21

A matrix-form complex variable method for multiple non-circular tunnels in layered media

Authors: Ye, Zi Kun, Ai, Zhi Yong ^⁎

Source: In Applied Mathematical Modelling July 2024 131:570-595

Analytical solution to stress intensity factors of cracks on both sides of a triangular hole in an infinite plate

Authors: Bi, Shengfan, Huang, Yong ^⁎, Wang, Hao

Source: In Theoretical and Applied Fracture Mechanics June 2024 131

Analytical Solution to the Seepage Field of Two Parallel Noncircular Tunnels in Permeable Anisotropic Ground

Authors: Wei, Fengran, Wang, Huaning^{Aff1, IDs1220502200540_cor2}, Zeng, Guangshang, Jiang, Mingjing

Source: KSCE Journal of Civil Engineering. 26(12):5328-5341

The Math of Liberation

Authors: Emmerson, Parker

Subject Terms: geometry, velocity phenomenologically, curvature dimensionality, circles, Data science, Harmonic analysis, advances in science, Differential topology, insight, non-commuatative, applied mathematics, mathematical logic, logical relationships, fabricated dimensions, universal order, Markov chains, mathematical foundations, quantum mechanics, Finite element analysis, mathematical methods, phenomenological velocity, instantaneous velocity, confined, Symmetry groups, field of study, Fourier analysis, algebraic, Statistical modeling, Convex optimization, Geometric combinatorics, non-ordinary realm, language of algebra, reality primacy, l α, q, r, θ, c variable, real analysis, Set theory, Real analysis, physics, discernment, Measure theoretic probability, computation, defining dimensions, ordering logic, theoretical framework, foundations, Spectral analysis, Computational geometry, true solution, Theoretical computer science, Stochastic processes, Fluid dynamics, Fractal dynamics, Linear programming, Machine learning, real virtuality beings, logical propositions, solution, dimensional fabrication, mathematical truths, law of commutation, parameters, circumferences, special relativity, objective reality, Mathematical finance, Euclidean geometry, mathematical structures, Graph theory, conceptual structures, Differential geometric spelunking, Intuitive mathematics, Probability distributions, mathematical representation, hidden variable, conceptual system, derivatives, Cryptography, laws of nature, geometric mean velocity, cognition, validity, definitions, mathematical understanding, geometrically, information, geometric mean time unit, higher mathematics, unified theory, universal laws, motion, semantics, interpretation, theories, calculus, angular averages, Numerical linear algebra, algebraically constructed, arc length difference, Discrete mathematics, Quantum field theory, infinity, physical systems, differential velocity space, Spectral geometry, Discrete optimization, Random matrices, Vector calculus, Algebraic topology, Numerical analysis, Parallel computing, Optimization, fundamental forces, musical applications, foundation, coherent expressions, oretical infusion, articulated ideas, Number theory, transcendental essence, physical explanations, integration of form, Computational number theory, phenomenal consciousness, mathematical, interesting results, Differential geometry, philosophical essence, event ordering, philosophical framework, constrained, Graph algorithms, transcendence, non-commutativity, logic, average velocity, Functional analysis, algebraic reality, physical laws, differential equations, Representation theory, nature, extraordinary magnitude, space, Fourier series, fundamental reality, Statistical learning, transcendental principles, Fractal geometry, qualitative evaluations, semiotics, Combinatorics, scientific explanations, Computational mathematics, instantanoues velocity, universal principles, Statistical inference, gestalt cosmology, Combinatorial optimization, integrated fields, dimensionality concept, Complex analysis, Topology, height function, square root, Elliptic curves, mathematical applications, reality, Theory of computation, Hilbert spaces, empirical discoveries, specific magnitudes, relativistic transformation, theoretical concepts, applied mathematic, Lorentz coefficient, universe, algebraically implied dimension, conceptual understanding, Computational complexity, mathematical formulations, fundamental principles, Mathematical physics, mathematical limitations, Matrix analysis, quantum mechanical paradigm, real light, Differential equations, mathematical reality, velocity, architecture, applications, Math of Liberation, Complex variable theory, difference, patterns of reality, subjective understanding, variable w, Numerical optimization, physical phenomena, quantum mechanical, human understanding, mathematical equations, intellectual intuition, alternative perceptions, Measure theory, angular time allocations, fundamental laws, embedded, transcendent forms, coefficients, conceptual frameworks, spatial essence, language, mathematical predictions, Lie groups, evidence, axiomatic systems, cone expression, Non-Euclidean geometry, velocity curvature, physical universe, Probability theory, Fuzzy logic, Continuous optimization, Quaternion algebra, full real analysis, concept of number, Dynamical systems theory, Group theory, metaphysical theories, Information geometry, principles of symmetry, cosmology, arc lengths, Algebraic coding theory, knowledge, abstract concepts, mathematical facts, new mathematics, perception, hidden variables, algebraic rearrangement, Decision theory, mathematical principles, Applied probability, harmonies, scientific inquiry, Dynamical systems, subset, Complex dynamical systems, deifferentiation, individual, conceptualization, Game theory, Theory of computable functions, diagrammed, Hermite polynomials, internal logic, mathematics, scientific theories, existential limitations, geometric perspectives, Chaos theory, mathematical concepts, method of argument, conceptual systems, data, Geometric algorithms, mathematics philosophy, human intuition, mathematical models, Regression analysis, mathematical reasoning, Ordinary differential equations, theoretical insights, mathematical descriptions, Abstract algebra, difference formula, Information theory, mathematical properties, universal construct, arbitrary measures, Cryptographic protocols, physical logic, arc length, Number theory algorithms, Multivariate calculus, angle, arbitrary radius, scientific developments, experiential reality, mathematical insights, theoretical constructs, conceptual reality, transcendental idealism, Distributional semantics, philosophy, circle difference equation, observable patterns, fundamental structures, observatory dark matter, intuitive understanding, interrelated patterns, acceleration, Linear algebraic groups, empirical evidence, non-commutation, Algebraic geometry, physical theories, Nonlinear dynamics, Network theory, mathematical entities, Statistical mechanics, concept, transcendental relativity, pure mathematical

Analytical stress solution and mechanical properties for rock mass containing a hole with complex shape

Authors: Tan, Lihai ^{a, b, c}, Ren, Ting ^c, Dou, Linming ^{a, b}, Yang, Xiaohan ^{c, ⁎}, Qiao, Ming ^c, Peng, Huaide ^d

Source: In Theoretical and Applied Fracture Mechanics August 2021 114

Analytical prediction of time-dependent behavior for tunneling-induced ground movements and stresses subjected to surcharge loading based on rheological mechanics

Authors: Zhang, Zhiguo ^{a, b, ⁎}, Huang, Maosong ^c, Pan, Yutao ^{b, d}, Jiang, Kangming ^a, Li, Zhenbo ^a, Ma, Shaokun ^e, Zhang, Yangbin ^a

Source: In Computers and Geotechnics January 2021 129

Analytical Predictions on the Ground Responses Induced by Shallow Tunneling Adjacent to a Pile Group

Authors: Caixia Guo, Yingying Tao, Fanchao Kong, Leilei Shi, Dechun Lu, Xiuli Du

Source: Mathematics, Vol 11, Iss 7, p 1608 (2023)

Subject Terms: adjacent crossing, complex variable theory, pile group, shallow tunnel, plastic zone, Mathematics, QA1-939

Relation: https://www.mdpi.com/2227-7390/11/7/1608; https://doaj.org/toc/2227-7390; https://doaj.org/article/cd8bac6c138a4086b96e1ad099c0c930

Availability: https://doi.org/10.3390/math11071608
https://doaj.org/article/cd8bac6c138a4086b96e1ad099c0c930

An Elastic Solution for Twin Circular Tunnels’ Stress in Hydrostatic Stress Field

Authors: Guo, Zihong^{Aff1, Aff2, Aff3, IDs10706021017565_cor1}, Liu, Xinrong, Zhu, Zhanyuan^{Aff1, Aff3}

Source: Geotechnical and Geological Engineering: An International Journal. 39(6):4253-4263

A comprehensive study of fracture evolution of brittle rock containing an inverted U-shaped cavity under uniaxial compression

Authors: Wu, Hao ^{a, c}, Kulatilake, Pinnaduwa H.S.W. ^{b, c}, Zhao, Guoyan ^{a, ⁎}, Liang, Weizhang ^a, Wang, Enjie ^a

Source: In Computers and Geotechnics December 2019 116

Stress distribution and fracture evolution around a trapezoidal cavity in sandstone loaded in compression

Authors: Wu, Hao ^{a, c}, Kulatilake, Pinnaduwa H.S.W. ^{b, c}, Zhao, Guoyan ^{a, ⁎}, Liang, Weizhang ^a

Source: In Theoretical and Applied Fracture Mechanics December 2019 104

A general analytical solution for lateral soil response of non-circular cross-sectional pile segment

Authors: Zhou, Hang ^⁎, Yuan, Jingrong, Liu, Hanlong

Source: In Applied Mathematical Modelling July 2019 71:601-631

Analytical elastic stress solution and plastic zone estimation for a pressure-relief circular tunnel using complex variable methods

Authors: Xu, Miao-Fei ^{a, b}, Wu, Shun-Chuan ^{a, b, ⁎}, Gao, Yong-Tao ^b, Ma, Jun ^c, Wu, Qing-Liang ^c

Source: In Tunnelling and Underground Space Technology incorporating Trenchless Technology Research February 2019 84:381-398

Analytical solutions for stress and displacement around inclined rectangular stopes with a large width-to-height ratio by the complex variable theory

Authors: Li, Yuanhui^{Aff1, Aff2, Aff3}, Xiong, Zhipeng^{Aff1, IDs12517022101827_cor2}, Li, Kunmeng^{Aff1, Aff2}, Jiang, Kaiyuan, Yu, Pengfei

Source: Arabian Journal of Geosciences. 15(9)

Analytical solution and numerical verification for the pressure-relief method of a circular tunnel

Authors: Shunchuan, Wu, Miaofei, Xu, Yongtao, Gao, Shihuai, Zhang, Fan, Chen

Source: Engineering Review : Međunarodni časopis namijenjen publiciranju originalnih istraživanja s aspekta analize konstrukcija, materijala i novih tehnologija u području strojarstva, brodogradnje, temeljnih tehničkih znanosti, elektrotehnike, računarstva i građevinarstva
Volume 38
Issue 3

Subject Terms: analytical solution, intersection, pressure relief, 13. Climate action, 4. Education, 11. Sustainability, complex variable theory, FLAC2D

File Description: application/pdf

Access URL: https://hrcak.srce.hr/file/296233
https://er.riteh.hr/index.php/ER/article/view/849
https://hrcak.srce.hr/201155
https://hrcak.srce.hr/file/296233
https://er.riteh.hr/index.php/ER/article/download/849/525

On the solution of a contact problem for a rhombus weakened with a full-strength hole

Authors: Odishelidze, Nana, Criado-Aldeanueva, Francisco, Sánchez-Sáez, José María

Source: RIUMA. Repositorio Institucional de la Universidad de Málaga
Universidad de Málaga

Subject Terms: stress state, 0203 mechanical engineering, Elasticidad, complex variable theory, 02 engineering and technology, 0101 mathematics, plate elasticity theory, 01 natural sciences

Access URL: http://scientiairanica.sharif.edu/article_4024.html
http://scientiairanica.sharif.edu/article_4024_5b4ed397974731640dfc71a0985f1d2e.pdf
https://hdl.handle.net/10630/37040

Solution of a problem of plane theory of elasticity for a square domain with a partially unknown boundary: A problem of plane theory of elasticity for a square domain

Authors: Odishelidze, Nana, Criado-Aldeanueva, Francisco, Sánchez-Sáez, José María

Source: RIUMA. Repositorio Institucional de la Universidad de Málaga
Universidad de Málaga

Subject Terms: Full-strength, stress state, mixed problem, 0203 mechanical engineering, 0103 physical sciences, Placas y cáscaras elásticas, complex variable theory, elasticity, 02 engineering and technology, 01 natural sciences

Access URL: https://hdl.handle.net/10630/33895
https://ui.adsabs.harvard.edu/abs/2017ZaMM...97..655O/abstract
http://onlinelibrary.wiley.com/doi/10.1002/zamm.201600072/abstract

Complex Variables and Laplace Transforms

Authors: Dyke, Phil^Aff8

Contributors: Chaplain, M.A.J., Series editor^Aff1, Erdmann, K., Series editor^Aff2, MacIntyre, Angus, Series editor^Aff3, Süli, Endre, Series editor^Aff4, Tehranchi, M R, Series editor^Aff5, Toland, J.F., Series editor^Aff6, Dyke, Phil^Aff7

Source: An Introduction to Laplace Transforms and Fourier Series. :209-237