Port-Hamiltonian formulation and symplectic discretization of Plate models. Part I : Mindlin model for thick plates

Abstract

The port-Hamiltonian formulation is a powerful method for modeling and interconnecting systems of different natures. In this paper, the port-Hamiltonian formulation in tensorial form of a thick plate described by the Mindlin-Reissner model is presented. Boundary control and observation are taken into account. Thanks to tensorial calculus, it can be seen that the Mindlin plate model mimics the interconnection structure of its one-dimensional counterpart, i.e. the Timoshenko beam. The Partitioned Finite Element Method (PFEM) is then extended to both the vectorial and tensorial formulations in order to obtain a suitable, i.e. structure-preserving, finite-dimensional port-Hamiltonian system (PHs), which preserves the structure and properties of the original distributed parameter system. Mixed boundary conditions are finally handled by introducing some algebraic constraints. Numerical examples are finally presented to validate this approach.

References in corpus (6)

• Weak Form of Stokes-Dirac Structures and Geometric Discretization of Port-Hamiltonian Systems
• Discrete Exterior Geometry Approach to Structure-Preserving Discretization of Distributed-Parameter Port-Hamiltonian Systems
• Stability and Stabilization of Infinite-dimensional Linear Port-Hamiltonian Systems
• A parallel edge orientation algorithm for quadrilateral meshes
• Linear wave systems on $n$-D spatial domains
• On the extraction of the boundary conditions and the boundary ports in second-order field theories

Cited by in corpus (8)

• A Partitioned Finite Element Method for power-preserving discretization of open systems of conservation laws
• Port-Hamiltonian formulation and symplectic discretization of plate models. Part II : Kirchhoff model for thin plates
• A port-Hamiltonian approach to modeling the structural dynamics of complex systems
• Well-posedness of linear first order Port-Hamiltonian Systems on multidimensional spatial domains
• Port-Hamiltonian flexible multibody dynamics
• A linearly-implicit energy-momentum preserving scheme for geometrically nonlinear mechanics based on non-canonical Hamiltonian formulations
• Energy-based Control and Observer Design for higher-order infinite-dimensional Port-Hamiltonian Systems
• Mixed formulation and structure-preserving discretization of Cosserat rod dynamics in a port-Hamiltonian framework