Consequences of Analyticity in Linear Elastostatics and Related Systems

We develop a Papkovich-Neuber type representation formula for the solutions of the Navier-Lamé equation of linear elastostatics for spatial star-shaped domains. This representation is compared to the existing ones.

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Real-Time Computer Simulation of Three Dimensional Elastostatics Using the Finite Point Method

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.110-116.2740 ◽

2011 ◽

Vol 110-116 ◽

pp. 2740-2745

Author(s):

Kirana Kumara P. ◽

Ashitava Ghosal

Keyword(s):

Real Time ◽

Graphics Processing Unit ◽

Numerical Technique ◽

Three Dimensional ◽

Point Method ◽

Processing Unit ◽

Finite Point ◽

Deformable Solids ◽

Finite Point Method ◽

Linear Elastostatics

Real-time simulation of deformable solids is essential for some applications such as biological organ simulations for surgical simulators. In this work, deformable solids are approximated to be linear elastic, and an easy and straight forward numerical technique, the Finite Point Method (FPM), is used to model three dimensional linear elastostatics. Graphics Processing Unit (GPU) is used to accelerate computations. Results show that the Finite Point Method, together with GPU, can compute three dimensional linear elastostatic responses of solids at rates suitable for real-time graphics, for solids represented by reasonable number of points.

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On the Asymptotic Behavior of D-Solutions to the Displacement Problem of Linear Elastostatics in Exterior Domains

Mathematics ◽

10.3390/math8010077 ◽

2020 ◽

Vol 8 (1) ◽

pp. 77

Author(s):

Vincenzo Coscia

Keyword(s):

Asymptotic Behavior ◽

Lipschitz Domain ◽

Three Dimensional ◽

Finite Energy ◽

Asymptotic Behavior Of Solutions ◽

Exterior Domains ◽

Displacement Problem ◽

Linear Elastostatics

We study the asymptotic behavior of solutions with finite energy to the displacement problem of linear elastostatics in a three-dimensional exterior Lipschitz domain.

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On the Fredholm Property of the Trace Operators Associated with the Elastic Layer Potentials

Mathematics ◽

10.3390/math7020134 ◽

2019 ◽

Vol 7 (2) ◽

pp. 134 ◽

Cited By ~ 3

Author(s):

Giulio Starita ◽

Alfonsina Tartaglione

Keyword(s):

Elastic Body ◽

Elastic Layer ◽

Fredholm Property ◽

System Of Equations ◽

Layer Potentials ◽

Connected Set ◽

Equilibrium Configurations ◽

Linear Elastostatics ◽

Class C

We deal with the system of equations of linear elastostatics, governing the equilibrium configurations of a linearly elastic body. We recall the basics of the theory of the elastic layer potentials and we extend the trace operators associated with the layer potentials to suitable sets of singular densities. We prove that the trace operators defined, for example, on W 1 − k − 1 / q , q ( ∂ Ω ) (with k ≥ 2 , q ∈ ( 1 , + ∞ ) and Ω an open connected set of R 3 of class C k ), satisfy the Fredholm property.

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Multiple and maximal periodicity in linear elastostatics

Journal of Elasticity ◽

10.1007/bf00041759 ◽

1986 ◽

Vol 16 (4) ◽

pp. 333-347

Author(s):

Kenneth B. Howell

Keyword(s):

Linear Elastostatics

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On the traction problem for linear elastostatics in exterior domains

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s030821050002045x ◽

1984 ◽

Vol 96 (1-2) ◽

pp. 55-64 ◽

Cited By ~ 2

Author(s):

Mariarosaria Padula

Keyword(s):

Continuous Dependence ◽

Body Force ◽

The Body ◽

Well Posedness ◽

Exterior Domains ◽

Homogeneous Case ◽

Linear Elastostatics

SynopsisIn this note, we study the well-posedness of the exterior traction value problem for linear anisotropic non-homogeneous elastostatics. We prove existence and continuous dependence upon the data. In particular, in the isotropic homogeneous case, provided the body force is “simple”, we show that solutions tend to zero uniformly at large spatial distances.

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