Search results for "elastodynamics"
showing 8 items of 8 documents
On the accuracy of the fast hierarchical DBEM for the analysis of static and dynamic crack problems
2010
In this paper the main features of a fast dual boundary element method based on the use of hierarchical matrices and iterative solvers are described and its effectiveness for fracture mechanics problems, both in the static and dynamic case, is demonstrated. The fast solver is built by representing the collocation matrix in hierarchical format and by using a preconditioned GMRES for the solution of the algebraic system. The preconditioner is computed in hierarchical format by LU decomposition of a coarse hierarchical representation of the collocation matrix. The method is applied to elastostatic problems and to elastodynamic cases represented in the Laplace transform domain. The application …
Hierarchical-ACA DBEM for anisotropic three-dimensional time-domain fracture mechanics
2012
Modeling wave propagation in elastic solids via high-order accurate implicit-mesh discontinuous Galerkin methods
2022
A high-order accurate implicit-mesh discontinuous Galerkin framework for wave propagation in single-phase and bi-phase solids is presented. The framework belongs to the embedded-boundary techniques and its novelty regards the spatial discretization, which enables boundary and interface conditions to be enforced with high-order accuracy on curved embedded geometries. High-order accuracy is achieved via high-order quadrature rules for implicitly-defined domains and boundaries, whilst a cell-merging strategy addresses the presence of small cut cells. The framework is used to discretize the governing equations of elastodynamics, written using a first-order hyperbolic momentum-strain formulation…
HHT-α and TR-BDF2 schemes for dynamic contact problems
2023
This work focuses on the numerical performance of HHT-α and TR-BDF2 schemes for dynamic frictionless unilateral contact problems between an elastic body and a rigid obstacle. Nitsche's method, the penalty method, and the augmented Lagrangian method are considered to handle unilateral contact conditions. Analysis of the convergence of an opposed value of the parameter α for the HHT-α method is achieved. The mass redistribution method has also been tested and compared with the standard mass matrix. Numerical results for 1D and 3D benchmarks show the functionality of the combinations of schemes and methods used.
A fast BEM for the analysis of plates with bonded piezoelectric patches
2010
In this paper a fast boundary element method for the elastodynamic analysis of 3D structures with bonded piezoelectric patches is presented. The elastodynamic analysis is performed in the Laplace domain and the time history of the relevant quantities is obtained by inverse Laplace transform. The bonded patches are modelled using a semi-analytical state-space variational approach. The computational features of the technique, in terms of required storage memory and solution time, are improved by a fast solver based on the use of hierarchical matrices. The presented numerical results show the potential of the technique in the study of structural health monitoring (SHM) systems.
Cloaking In-Plane Elastic Waves with Swiss Rolls
2020
We propose a design of cylindrical cloak for coupled in-plane shear waves consisting of concentric layers of sub-wavelength resonant stress-free inclusions shaped as Swiss rolls. The scaling factor between inclusions&rsquo
A fast hierarchical dual boundary element method for three-dimensional elastodynamic crack problems
2010
In this work a fast solver for large-scale three-dimensional elastodynamic crack problems is presented, implemented, and tested. The dual boundary element method in the Laplace transform domain is used for the accurate dynamic analysis of cracked bodies. The fast solution procedure is based on the use of hierarchical matrices for the representation of the collocation matrix for each computed value of the Laplace parameter. An ACA (adaptive cross approximation) algorithm is used for the population of the low rank blocks and its performance at varying Laplace parameters is investigated. A preconditioned GMRES is used for the solution of the resulting algebraic system of equations. The precond…