Dynamical systems and topology optimization

Klarbring, Anders; Torstenfelt, Bo

doi:10.1007/s00158-010-0479-9

Cited by 28 publications

(7 citation statements)

References 24 publications

(67 reference statements)

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“…Moreover, a mathematical structure that is essentially identical to that of the SIMP method is found in bone remodeling models, see Harrigan and Hamilton . This one‐to‐one relation between theories has been discussed in Klarbring and Torstenfelt .…”

Section: State Problem and Configurational Variablesmentioning

confidence: 92%

“…An explicit example of an objective function

f (u, bold-italicρ)

that is used in stiffness structural optimization and which also turns out to be involved in bone remodeling, , is the following:

f_{G} (ρ, bold-italicu) = \frac{1}{2} F^{T} u + μ \sum_{i = 1}^{E} a_{i} ρ_{i} .

The first term is usually known as compliance. The objective associated with this term is to minimize the projection of the displacement on the direction of the given load.…”

Section: Dynamical Systems Approachmentioning

confidence: 99%

“…An explicit example of an objective function f (u, ρ) that is used in stiffness structural optimization and which also turns out to be involved in bone remodeling, [16][17][18], is the following:…”

Section: Special Objective Functionsmentioning

confidence: 99%

“…That is, there exists a positive definite matrix E(ρ) such that h = E(ρ)Bμ. (16) Inserting this constitutive law into the balance law (10) and using the necessary condition (13) for the chemical potential, we getċ…”

Section: Wwwzamm-journalorgmentioning

confidence: 99%

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Nutrient modulated structural design with application to growth and degradation

2015

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Phenomena such as biological growth and damage evolution can be thought of as time evolving processes, the directions of which are governed by descendent of certain goal functions. Mathematically this means using a dynamical systems approach to optimization. We extend such an approach by introducing a field quantity, representing nutrients or other non‐mechanical stimuli, that modulate growth and damage evolution. The derivation of a generic model is systematic, starting from a Lyaponov‐type descent condition and utilizing a Coleman‐Noll strategy. A numerical algorithm for finding stationary points of the resulting dynamical system is suggested and applied to two model problems where the influence of different levels of nutrient sensitivity are observed. The paper demonstrates the use of a new modeling technique and shows its application in deriving a generic problem of growth and damage evolution.

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Section: State Problem and Configurational Variablesmentioning

confidence: 92%

“…An explicit example of an objective function

f (u, bold-italicρ)

that is used in stiffness structural optimization and which also turns out to be involved in bone remodeling, , is the following:

f_{G} (ρ, bold-italicu) = \frac{1}{2} F^{T} u + μ \sum_{i = 1}^{E} a_{i} ρ_{i} .

The first term is usually known as compliance. The objective associated with this term is to minimize the projection of the displacement on the direction of the given load.…”

Section: Dynamical Systems Approachmentioning

confidence: 99%

Section: Special Objective Functionsmentioning

confidence: 99%

Section: Wwwzamm-journalorgmentioning

confidence: 99%

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Nutrient modulated structural design with application to growth and degradation

2015

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“…A structural optimisation viewpoint on evolution can be determined using optimality principles instead of evolution laws, see [10]. Thus, design space models and variational design sensitivity analysis based on an improved formulation of continuum mechanics contribute significantly to an enhanced formulation, see [11,12].…”

Section: Introductionmentioning

confidence: 99%

A structural optimisation viewpoint on growth phenomena

Barthold¹

2012

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Evolutionary solid bodies undergoing changes of mass, of properties, and of shapes are considered in models of growth and adaptation and similarily in structural optimisation. A fundamental separation of different growth phenomena and a subsequent parametrisation using independent design variables for the amount of substance as well as for molar mass and molar volume facilitates an efficient formulation of the design space. Thus, the effects of design variations, i.e. change of amount of substance, on the variations of the structural response, i.e. the deformation in physical space, can be clearly described. Overall, a novel treatment of growth processes based on an evolution of the amount of substance is outlined. The parallelism of variations in physical and design space are highlighted and compared with the multiplicative decomposition of the deformation gradient into a growth and an elastic part incorporating an incompatible intermediate configuration. This drawback is overcome by a compatible manifold based on material points modelling the amount of substance outside of any geometrical space.

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Slime Mould Inspired Models for Path Planning: Collective and Structural Approaches

Jones

Safonov

2018

Emergence, Complexity and Computation

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Dynamical systems and topology optimization

Cited by 28 publications

References 24 publications

Nutrient modulated structural design with application to growth and degradation

Nutrient modulated structural design with application to growth and degradation

A structural optimisation viewpoint on growth phenomena

Slime Mould Inspired Models for Path Planning: Collective and Structural Approaches

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