Optimized Schwarz Methods for Linear Elasticity and Overlumping
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Elasticity
Linear elasticity
Nonlinear elasticity
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Nonlinear elasticity
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Linear elasticity
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Nonlinear elasticity
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This lecture intends to describe the asymptotic behaviour of the displacement in a linear elastic body containing either a thin non-linear elastic layer or thin reinforcing fibres, when the thinness of these layer or fibres tends to 0. The main purpose of this talk is to present the functional analysis which leads to these asymptotic results in the framework of linear elasticity.
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This paper examines the effects of relaxing the assumption of classical linear elasticity that the loads act in their entirety on the undeformed shape. Instead, loads here are applied incrementally as deformation proceeds, and resulting fields are integrated. A formal statement of the attendant integrated elasticity theory is provided. A class of problems is identified for which this formulation is amenable to solution in closed form. Some results from these configurations are compared with linear elasticity and experimentally measured data. The comparisons indicate that, as deformation increases, integrated elasticity is capable of tracking the physical response better than linear elasticity.
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In this paper, we derive a dynamic surface elasticity model for the two-dimensional midsurface of a thin, three-dimensional, homogeneous, isotropic, nonlinear gradient elastic plate of thickness $h$. The resulting model is parameterized by five, conceivably measurable, physical properties of the plate, and the stored surface energy reduces to Koiter's plate energy in a singular limiting case. The model corrects a theoretical issue found in wave propagation in thin sheets and, when combined with the author's theory of Green elastic bodies possessing gradient elastic material boundary surfaces, removes the singularities present in fracture within traditional/classical models. Our approach diverges from previous research on thin shells and plates, which primarily concentrated on deriving elasticity theories for material surfaces from classical three-dimensional Green elasticity. This work is the first in rigorously developing a surface elasticity model based on a parent nonlinear gradient elasticity theory.
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Nonlinear elasticity
Linear elasticity
Elastic energy
Limiting
Plate theory
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Linear elasticity
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Bar (unit)
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Abstract Solutions are given to four two‐dimensional exterior problems in a linear, mechanically homogeneous, isotropic and centrosymmetric elastic solid of grade two (Toupin [1], p. 87). bounded internally by a circular cylindrical cavity. The solutions are found to be size dependent and to exhibit boundary layer effects. The results are compared to the corresponding results in classical elasticity, couple‐stress theory and micropolar elasticity.
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In this paper we solve a simple dead load problem for an isotropic constrained material according to the linearized finite theory of elasticity. We show that the solution of such a problem can be obtained by linearizing with re- spect to the displacement gradient the solution of the corresponding problem in finite elasticity for an isotropic material subject to the same constraint, exactly as occurs for the constitutive equations of the two theories. On the contrary, the solution of the same dead load problem provided by the classical linear elasticity for constrained materials can be obtained by the solution of the corresponding problem for the unconstrained linear elastic material for limiting behaviour of suitable elastic moduli. The same applies for the constitutive equations of the classical linear elasticity for constrained materials: they are derived by those of the linear elasticity for unconstrained materials for limiting values of some elastic modulus. Finally we compare the solutions in finite elasticity, linearized finite theory of elasticity, classical linear elasticity for constrained materials and we show that they are in agreement with different hypotheses on the prescribed loads.
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Linear elasticity
Limiting
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