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Design-dependent loads in topology optimization

Blaise Bourdin, Antonin Chambolle (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We present, analyze, and implement a new method for the design of the stiffest structure subject to a pressure load or a given field of internal forces. Our structure is represented as a subset S of a reference domain, and the complement of S is made of two other “phases”, the “void” and a fictitious “liquid” that exerts a pressure force on its interface with the solid structure. The problem we consider is to minimize the compliance of the structure S, which is the total work of the pressure...

Determination of creep, fatigue and activation energy from constant strain-rate experiments

Michele Caputo (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si interpretano i risultati degli esperimenti fatti su mezzi anelastici mediante applicazione di deformazioni crescenti linearmente nel tempo. Si trova che dai risultati di questi esperimenti, si può risalire alla funzione di creep che viene determinata con tre diversi modelli di approssimazione. Si trova inoltre che per decidere sul comportamento a lungo termine dei materiali sono necessari esperimenti a più lungo termine di quelli fatti. Si dimostra poi che le relazioni classiche che rappresentano...

Determination of the initial stress tensor from deformation of underground opening in excavation process

Josef Malík, Alexej Kolcun (2022)

Applications of Mathematics

A method for the detection of the initial stress tensor is proposed. The method is based on measuring distances between pairs of points located on the wall of underground opening in the excavation process. This methods is based on solving twelve auxiliary problems in the theory of elasticity with force boundary conditions, which is done using the least squares method. The optimal location of the pairs of points on the wall of underground openings is studied. The pairs must be located so that the...

Determination of the initial stress tensor from deformation of underground opening -- theoretical background and applications

Malík, Josef, Kolcun, Alexej (2023)

Programs and Algorithms of Numerical Mathematics

In this paper a method for the detection of initial stress tensor is proposed. The method is based on measuring distances between some pairs of points located on the wall of underground opening in the excavation process. This methods is based on the solution of eighteen auxiliary problems in the theory of elasticity with force boundary conditions. The optimal location of the pairs of points on the wall of underground work is studied. The pairs must be located so that the condition number of a certain...

Determination of the Thickness and Composition Profiles for a Film of Binary Mixture on a Solid Substrate

L. Fraštia, U. Thiele, L. M. Pismen (2010)

Mathematical Modelling of Natural Phenomena

We determine the steady-state structures that result from liquid-liquid demixing in a free surface film of binary liquid on a solid substrate. The considered model corresponds to the static limit of the diffuse interface theory describing the phase separation process for a binary liquid (model-H), when supplemented by boundary conditions at the free surface and taking the influence of the solid substrate into account. The resulting variational problem...

Development of three dimensional constitutive theories based on lower dimensional experimental data

Satish Karra, Kumbakonam R. Rajagopal (2009)

Applications of Mathematics

Most three dimensional constitutive relations that have been developed to describe the behavior of bodies are correlated against one dimensional and two dimensional experiments. What is usually lost sight of is the fact that infinity of such three dimensional models may be able to explain these experiments that are lower dimensional. Recently, the notion of maximization of the rate of entropy production has been used to obtain constitutive relations based on the choice of the stored energy and rate...

Dewetting dynamics of anisotropic particles: A level set numerical approach

Siddharth Gavhale, Karel Švadlenka (2022)

Applications of Mathematics

We extend thresholding methods for numerical realization of mean curvature flow on obstacles to the anisotropic setting where interfacial energy depends on the orientation of the interface. This type of schemes treats the interface implicitly, which supports natural implementation of topology changes, such as merging and splitting, and makes the approach attractive for applications in material science. The main tool in the new scheme are convolution kernels developed in previous studies that approximate...

Direct approach to mean-curvature flow with topological changes

Petr Pauš, Michal Beneš (2009)

Kybernetika

This contribution deals with the numerical simulation of dislocation dynamics. Dislocations are described by means of the evolution of a family of closed or open smooth curves Γ ( t ) : S → ℝ 2 , t ≧ 0 . The curves are driven by the normal velocity v which is the function of curvature κ and the position. The evolution law reads as: v = - κ + F . The motion law is treated using direct approach numerically solved by two schemes, i. e., backward Euler semi-implicit and semi-discrete method of lines. Numerical stability is improved...

Discontinuous Galerkin and the Crouzeix–Raviart element : application to elasticity

Peter Hansbo, Mats G. Larson (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We propose a discontinuous Galerkin method for linear elasticity, based on discontinuous piecewise linear approximation of the displacements. We show optimal order a priori error estimates, uniform in the incompressible limit, and thus locking is avoided. The discontinuous Galerkin method is closely related to the non-conforming Crouzeix–Raviart (CR) element, which in fact is obtained when one of the stabilizing parameters tends to infinity. In the case of the elasticity operator, for which the...

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