Caleta Numérica
Caleta Numérica
A Locking-Free DPG Scheme for Timoshenko Beams
A Locking-Free DPG Scheme for Timoshenko Beams
Carlos García, Pontificia Universidad Católlica de Chile
Carlos García, Pontificia Universidad Católlica de Chile
We develop a discontinuous Petrov–Galerkin scheme with optimal test functions (DPG method) for the Timoshenko beam bending model with various boundary conditions, combining clamped, supported, and free ends. Our scheme approximates the transverse deflection and bending moment. It converges quasi-optimally in $L^2$ and is locking free. In particular, it behaves well (converges quasi-optimally) in the limit case of the Euler–Bernoulli model. Several numerical results illustrate the performance of our method.
References
[1] C. Carstensen, L. Demkowicz and J. Gopalakrishnan, Breaking spaces and forms for the DPG method and applications including Maxwell equations. Computers and Mathematics with Applications, 72 (2016): pp. 494-522.
[2] L. Demkowicz and J. Gopalakrishnan, A class of discontinuous Petrov-Galerkin methods. Part II: Optimal test functions.Numerical Methods for Partial DierentialEquations, 27 (2011): pp. 70-105.
[3] L. Demkowicz and J. Gopalakrishnan, Analysis of the DPG method for the Poisson equation. SIAM J. Numer. Anal., 49 (2011): pp. 1788-1809.
[4] T. Fuhrer, N. Heuer, F. J. Sayas, An ultraweak formulation of the Reissner{Mindlin plate bending model and DPG approximation. Submitted.
[5] T. Fuhrer, N. Heuer, Fully discrete DPG methods for the Kirchhof-Love plate bending model. Comput. Methods Appl. Mech. Engrg., 343 (2019): pp. 550-571.
[6] T. Fuhrer, N. Heuer and A. Niemi, An ultraweak formulation of the Kirchhof Love plate bending model and DPG approximation. Math. Comp., 318 (2019): pp. 1587-1619.
[7] A. Niemi, J. Bramwell, L. Demkowicz, Discontinuous Petrov-Galerkin method with optimal test functions for thin{body problems in solid mechanics. Comput. Methods Appl. Mech. Engrg., 200 (2011): pp. 1291-1300.
[1] C. Carstensen, L. Demkowicz and J. Gopalakrishnan, Breaking spaces and forms for the DPG method and applications including Maxwell equations. Computers and Mathematics with Applications, 72 (2016): pp. 494-522.
[2] L. Demkowicz and J. Gopalakrishnan, A class of discontinuous Petrov-Galerkin methods. Part II: Optimal test functions.Numerical Methods for Partial DierentialEquations, 27 (2011): pp. 70-105.
[3] L. Demkowicz and J. Gopalakrishnan, Analysis of the DPG method for the Poisson equation. SIAM J. Numer. Anal., 49 (2011): pp. 1788-1809.
[4] T. Fuhrer, N. Heuer, F. J. Sayas, An ultraweak formulation of the Reissner{Mindlin plate bending model and DPG approximation. Submitted.
[5] T. Fuhrer, N. Heuer, Fully discrete DPG methods for the Kirchhof-Love plate bending model. Comput. Methods Appl. Mech. Engrg., 343 (2019): pp. 550-571.
[6] T. Fuhrer, N. Heuer and A. Niemi, An ultraweak formulation of the Kirchhof Love plate bending model and DPG approximation. Math. Comp., 318 (2019): pp. 1587-1619.
[7] A. Niemi, J. Bramwell, L. Demkowicz, Discontinuous Petrov-Galerkin method with optimal test functions for thin{body problems in solid mechanics. Comput. Methods Appl. Mech. Engrg., 200 (2011): pp. 1291-1300.
We will meet in google meet, use the link below to connect with us
We will meet in google meet, use the link below to connect with us
June 12, 15:00 Chile, via https://meet.google.com/viw-rqds-ikc
June 12, 15:00 Chile, via https://meet.google.com/viw-rqds-ikc
If you are interested in giving a talk, please contact: paulina.sepulveda @pucv.cl
If you are interested in giving a talk, please contact: paulina.sepulveda @pucv.cl