scholarly journals MAKING USE OF SYMMETRIES IN THE THREE-DIMENSIONAL ELASTIC INVERSE HOMOGENIZATION PROBLEM

2019 ◽  
Vol 17 (3) ◽  
pp. 261-280 ◽  
Author(s):  
C. Méndez ◽  
J.M. Podestá ◽  
S. Toro ◽  
Alfredo E. Huespe ◽  
J. Oliver
Keyword(s):  
Three Dimensional ◽  
Inverse Homogenization ◽  
Homogenization Problem

scholarly journals Inverse homogenization using the topological derivative

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Àlex Ferrer ◽  
Sebastián Miguel Giusti
Keyword(s):  
Optimization Algorithms ◽  
Material Design ◽  
Topological Derivative ◽  
Gradient Algorithm ◽  
Optimal Topology ◽  
Inverse Homogenization ◽  
Homogenization Problem ◽  
Content Type ◽  
Classical Optimization ◽  
Derivative Concept

PurposeThe purpose of this study is to solve the inverse homogenization problem, or so-called material design problem, using the topological derivative concept.Design/methodology/approachThe optimal topology is obtained through a relaxed formulation of the problem by replacing the characteristic function with a continuous design variable, so-called density variable. The constitutive tensor is then parametrized with the density variable through an analytical interpolation scheme that is based on the topological derivative concept. The intermediate values that may appear in the optimal topologies are removed by penalizing the perimeter functional.FindingsThe optimization process benefits from the intermediate values that provide the proposed method reaching to solutions that the topological derivative had not been able to find before. In addition, the presented theory opens the path to propose a new framework of research where the topological derivative uses classical optimization algorithms.Originality/valueThe proposed methodology allows us to use the topological derivative concept for solving the inverse homogenization problem and to fulfil the optimality conditions of the problem with the use of classical optimization algorithms. The authors solved several material design examples through a projected gradient algorithm to show the advantages of the proposed method.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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