A port-Hamiltonian approach to modeling the structural dynamics of complex systems

Warsewa, Alexander; Böhm, Michael; Sawodny, Oliver; Tarín, Cristina

doi:10.1016/j.apm.2020.07.038

Cited by 10 publications

(4 citation statements)

References 26 publications

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“…Also the possibilities and advantages of the PH formulation for structural mechanics have already been shown in several articles, e.g. [6,21].…”

Section: Introductionmentioning

confidence: 89%

Explicit port-Hamiltonian FEM models for geometrically nonlinear mechanical systems

Thoma¹,

Kotyczka²

2022

Preprint

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In this article, we present the port-Hamiltonian representation, the structure preserving discretization and the resulting finitedimensional state space model of geometrically nonlinear mechanical systems based on a mixed finite element formulation. This article focuses on St. Venant-Kirchhoff materials connecting the Green strain and the second Piola-Kirchhoff stress tensor in a linear relationship which allows a port-Hamiltonian representation by means of its co-energy (effort) variables. Due to treatment of both Dirichlet and Neumann boundary conditions in the appropriate variational formulation, the resulting port-Hamiltonian state space model features both of them as explicit (control) inputs. Numerical experiments generated with FEniCS illustrate the properties of the resulting FE models.

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“…Also the possibilities and advantages of the PH formulation for structural mechanics have already been shown in several articles, e.g. [6,21].…”

Section: Introductionmentioning

confidence: 89%

Explicit port-Hamiltonian FEM models for geometrically nonlinear mechanical systems

Thoma¹,

Kotyczka²

2022

Preprint

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“…Due to its well-known beneficial properties [1], the port-Hamiltonian (PH) framework has gained large popularity also when modeling elastodynamical systems (which might occur in structural mechanics [2] or multibody system dynamics [3]). The developed models are able to describe multiphysical coupling as well as the interconnection to other subsystems, whilst achieving a systematic and power-preserving formulation.…”

Section: Introductionmentioning

confidence: 99%

Discrete nonlinear elastodynamics in a port‐Hamiltonian framework

Kinon,

Thoma,

Betsch

et al. 2023

Proc Appl Math and Mech

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We provide a fully nonlinear port‐Hamiltonian formulation for discrete elastodynamical systems as well as a structure‐preserving time discretization. The governing equations are obtained in a variational manner and represent index‐1 differential algebraic equations. Performing an index reduction, one obtains the port‐Hamiltonian state space model, which features the nonlinear strains as an independent state next to position and velocity. Moreover, hyperelastic material behavior is captured in terms of a nonlinear stored energy function. The model exhibits passivity and losslessness and has an underlying symmetry yielding the conservation of angular momentum. We perform temporal discretization using the midpoint discrete gradient, such that the beneficial properties are inherited by the developed time stepping scheme in a discrete sense. The numerical results obtained in a representative example are demonstrated to validate the findings.

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“…see for example [42] for an application in the control of high-rise buildings. We observe that ker RQ ∩ im B = {0} holds; that is, the sufficient condition for regularity derived in [35] is satisfied.…”

Section: Introduction Since Their Introduction Inmentioning

confidence: 99%

Optimal Control of Port-Hamiltonian Descriptor Systems with Minimal Energy Supply

Faulwasser¹,

Maschke²,

Philipp³

et al. 2022

SIAM J. Control Optim.

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We study the problem of state transition on a finite time interval with minimal energy supply for linear port-Hamiltonian systems. While the cost functional of minimal energy supply is intrinsic to the port-Hamiltonian structure, the necessary conditions of optimality resulting from Pontryagin's maximum principle may yield singular arcs. The underlying reason is the linear dependence on the control, which makes the problem of determining the optimal control as a function of the state and the adjoint more complicated or even impossible. To resolve this issue, we fully characterize regularity of the (differential-algebraic) optimality system by using the interplay of the cost functional and the dynamics. In the regular case, we fully determine the control on the singular arc. Otherwise, we provide rank-minimal perturbations by a quadratic control cost such that the optimal control problem becomes regular. We illustrate the applicability of our results by a general second-order mechanical system and a discretized boundary-controlled heat equation.

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A port-Hamiltonian approach to modeling the structural dynamics of complex systems

Cited by 10 publications

References 26 publications

Explicit port-Hamiltonian FEM models for geometrically nonlinear mechanical systems

Explicit port-Hamiltonian FEM models for geometrically nonlinear mechanical systems

Discrete nonlinear elastodynamics in a port‐Hamiltonian framework

Optimal Control of Port-Hamiltonian Descriptor Systems with Minimal Energy Supply

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