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【仓储物流工程师,国电联合动力技术有限公司】前程无忧官方招聘网站
【仓储物流工程师,国电联合动力技术有限公司】前程无忧官方招聘网站
solid and fluid mechanics. For many of these problems least-squares principles offer many theoretical and computational advantages in the implementation of the corresponding finite element model that are not present in the traditional weak form Galerkin finite element model. For instance, the use of least-squares principles leads to a variational unconstrained minimization problem where compatibility conditions between approximation spaces never arise. Furthermore, the resulting linear algebraic problem will have a symmetric positive definite coefficient matrix, allowing the use of robust and fast iterative methods for its solution. We find that the use of high p-levels is beneficial in least-squares based finite element models and present guidelines to follow when a low p-level numerical solution is sought. Numerical examples in the context of incompressible and compressible viscous fluid flows, plate bending, and shear-deformable shells are presented to demonstrate the merits of the formulations.
Article Outline
1. Introduction
2. An abstract least-squares formulation
2.1. Notation
2.2. The abstract problem
2.3. L2 least-squares formulation
2.3.1. Space–time coupled formulation
2.3.2. Space–time decoupled formulation
2.4. The variational problem
2.5. The finite element model
2.6. Norm-equivalence and its implications
2.7. A least-squares collocation formulation
3. Viscous incompressible and compressible fluid flows
3.1. Governing equations
3.2. Kovasznay flow
3.3. Compressible flow past a NACA0012 airfoil
4. Plates and shells
4.1. Governing equations
4.2. Simply supported circular plate
4.3. Barrel vault
5. Summary and concluding remarks
References Purchase
154
Finite element modelling and updating of a lively footbridge: The complete process Original Research Article
Journal of Sound and Vibration, Volume 301, Issues 1-2, 20 March 2007, Pages 126-145
Stana ?ivanovi?, Aleksandar Pavic, Paul Reynolds
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