Search results for "Mathematical analysis"
showing 10 items of 2409 documents
The development of a hybrid technique employing the boundary element method for thermoelastic stress separation
2000
: This paper presents a development of a hybrid technique employing a boundary element method for determining individual stress components in two-dimensional arbitrarily shaped domains from experimental isopachics only. The procedure consists of a numerical solution of two Poisson equations representing equilibrium for two-dimensional plane-stressed solids with zero body forces. An existing technique is employed for smoothing interior thermoelastic data and enhancing boundary information. The algorithm of stress separation has been implemented with the help of commercial codes. The whole procedure has been tested through a complete post-processing example of thermoelastic stress analysis da…
One-dimensional heterogeneous solids with uncertain elastic modulus in presence of long-range interactions: Interval versus stochastic analysis
2013
The analysis of one-dimensional non-local elastic solids with uncertain Young's modulus is addressed. Non-local effects are represented as long-range central body forces between non-adjacent volume elements. For comparison purpose, the fluctuating elastic modulus of the material is modeled following both a probabilistic and a non-probabilistic approach. To this aim, a novel definition of the interval field concept, able to limit the overestimation affecting ordinary interval analysis, is introduced. Approximate closed-form expressions are derived for the bounds of the interval displacement field as well as for the mean-value and variance of the stochastic response.
Fundamental solutions for general anisotropic multi-field materials based on spherical harmonics expansions
2016
Abstract A unified method to evaluate the fundamental solutions for generally anisotropic multi-field materials is presented. Based on the relation between the Rayleigh expansion and the three-dimensional Fourier representation of a homogenous partial differential operator, the proposed technique allows to obtain the fundamental solutions and their derivatives up to the desired order as convergent series of spherical harmonics. For a given material, the coefficients of the series are computed only once, and the derivatives of the fundamental solutions are obtained without any term-by-term differentiation, making the proposed approach attractive for boundary integral formulations and efficie…
Stress gradient versus strain gradient constitutive models within elasticity
2014
Abstract A stress gradient elasticity theory is developed which is based on the Eringen method to address nonlocal elasticity by means of differential equations. By suitable thermodynamics arguments (involving the free enthalpy instead of the free internal energy), the restrictions on the related constitutive equations are determined, which include the well-known Eringen stress gradient constitutive equations, as well as the associated (so far uncertain) boundary conditions. The proposed theory exhibits complementary characters with respect to the analogous strain gradient elasticity theory. The associated boundary-value problem is shown to admit a unique solution characterized by a Helling…
Quadrature rules for qualocation
2003
Qualocation is a method for the numerical treatment of boundary integral equations on smooth curves which was developed by Chandler, Sloan and Wendland (1988-2000) [1,2]. They showed that the method needs symmetric J–point–quadrature rules on [0, 1] that are exact for a maximum number of 1–periodic functions The existence of 2–point–rules of that type was proven by Chandler and Sloan. For J ∈ {3, 4} such formulas have been calculated numerically in [2]. We show that the functions Gα form a Chebyshev–system on [0, 1/2] for arbitrary indices a and thus prove the existence of such quadrature rules for any J.
Государственная граница как пограничный объект в сети трансграничного сотрудничества: случай границы Латвии, Эстонии и России
2019
Цель публикации – раскрыть функции государственной границы в качестве пограничного объекта в сети трансграничного сотрудничества в случае внутренней и внешней границы ЕС.Теоретическое обрамление публикации составляет теория пограничных объектов – производное теории сети агентов, которую в своей работе «Институциональная экология, «интерпретация» и пограничные объекты: любители и профессионалы в зоологическом музее позвоночных в Беркли» (1989) развивали Сьюзaн Ли Стар и Джеймс Гриземер.Пограничные объекты как теоретическое понятие были созданы на основании взаимодействия различных социальных миров друг с другом и на точке, когда им необходима взаимная интерпретация (Worrall, 2010). Пограничн…
Bounded and unbounded solutions for a class of quasi-linear elliptic problems with a quadratic gradient term
2001
Abstract Our aim in this article is to study the following nonlinear elliptic Dirichlet problem: − div [a(x,u)·∇u]+b(x,u,∇u)=f, in Ω; u=0, on ∂Ω; where Ω is a bounded open subset of RN, with N>2, f∈L m (Ω) . Under wide conditions on functions a and b, we prove that there exists a type of solution for this problem; this is a bounded weak solution for m>N/2, and an unbounded entropy solution for N/2>m⩾2N/(N+2). Moreover, we show when this entropy solution is a weak one and when can be taken as test function in the weak formulation. We also study the summability of the solutions.
Boundary angles, cusps and conformal mappings
1986
Let f be a conformal mapping of a bounded Jordan domain D in the complex plane onto the unit disk . This paper examines the consequences for the local geometry of D near a boundary point z 0 of the mapping f-or, to be more precise, of the homeomorphic extension of this mapping to the closure of D—satisfying a Holder condition at z 0 or, alternatively, of its inverse satisfying a Holder condition at the point f(z 0). In particular, the compatibility of Holder conditions with the presence of cusps in the boundary of D is investigated.
Oscillatory integrals and fractal dimension
2021
Theory of singularities has been closely related with the study of oscillatory integrals. More precisely, the study of critical points is closely related to the study of asymptotic of oscillatory integrals. In our work we investigate the fractal properties of a geometrical representation of oscillatory integrals. We are motivated by a geometrical representation of Fresnel integrals by a spiral called the clothoid, and the idea to produce a classification of singularities using fractal dimension. Fresnel integrals are a well known class of oscillatory integrals. We consider oscillatory integral $$ I(\tau)=\int_{; ; \mathbb{; ; R}; ; ^n}; ; e^{; ; i\tau f(x)}; ; \phi(x) dx, $$ for large value…
Special Splines of Exponential Type for the Solutions of Mass Transfer Problems in Multilayer Domains
2016
We consider averaging methods for solving the 3-D boundary-value problem of second order in multilayer domain. The special hyperbolic and exponential type splines, with middle integral values of piece-wise smooth function interpolation are considered. With the help of these splines the problems of mathematical physics in 3-D with piece-wise coefficients are reduced with respect to one coordinate to 2-D problems. This procedure also allows to reduce the 2-D problems to 1-D problems and the solution of the approximated problemsa can be obtained analytically. In the case of constant piece-wise coefficients we obtain the exact discrete approximation of a steady-state 1-D boundary-value problem.…