Extended constraint enforcement formulations for finite-DOF systems based on Gauss’s principle of least constraint

2020 ◽  
Vol 101 (4) ◽  
pp. 2577-2597
Author(s):  
Renato Maia Matarazzo Orsino
Keyword(s):  
Constraint Enforcement

scholarly journals Comparing double-step and penalty-based semirecursive formulations for hydraulically actuated multibody systems in a monolithic approach

2021 ◽  
Author(s):  
Suraj Jaiswal ◽  
Jarkko Rahikainen ◽  
Qasim Khadim ◽  
Jussi Sopanen ◽  
Aki Mikkola
Keyword(s):  
Time Integration ◽  
Physical Nature ◽  
Double Step ◽  
Work Cycle ◽  
Driven System ◽  
Hydraulically Actuated ◽  
Fluid Theory ◽  
Monolithic Approach ◽  
Constraint Enforcement ◽  
Volume Size

AbstractThe simulation of mechanical systems often requires modeling of systems of other physical nature, such as hydraulics. In such systems, the numerical stiffness introduced by the hydraulics can become a significant aspect to consider in the modeling, as it can negatively effect to the computational efficiency. The hydraulic system can be described by using the lumped fluid theory. In this approach, a pressure can be integrated from a differential equation in which effective bulk modulus is divided by a volume size. This representation can lead to numerical stiffness as a consequence of which time integration of a hydraulically driven system becomes cumbersome. In this regard, the used multibody formulation plays an important role, as there are many different procedures for the constraint enforcement and different sets of coordinates to choose from. This paper introduces the double-step semirecursive approach and compares it with a penalty-based semirecursive approach in case of coupled multibody and hydraulic dynamics within the monolithic framework. To this end, hydraulically actuated four-bar and quick-return mechanisms are analyzed as case studies. The two approaches are compared in terms of the work cycle, energy balance, constraint violation, and numerical efficiency of the mechanisms. It is concluded that the penalty-based semirecursive approach has a number of advantages compared with the double-step semirecursive approach, which is in accordance with the literature.

Constraint Enforcement via Tube-Based MPC Exploiting Switching Restrictions

2021 ◽  
Author(s):  
Reza Lavaei ◽  
Richard Hall ◽  
Claus Danielson ◽  
Leila Bridgeman
Keyword(s):  
Constraint Enforcement

Section Translational Movement Imposition for Macroelements

2019 ◽  
Author(s):  
Rodrigo Provasi ◽  
Clóvis de Arruda Martins
Keyword(s):  
Boundary Conditions ◽  
Degrees Of Freedom ◽  
Rigid Bodies ◽  
Cylindrical Layer ◽  
Finite Element Program ◽  
Translational Movement ◽  
Specific Contact ◽  
Element Program ◽  
Contact Models ◽  
Constraint Enforcement

Abstract Boundary conditions play a very important role in any mathematical model. They heavily influence the response near the region they are, but the farther the interest region is, the less important the boundary condition influence becomes. Also, the response depends of which movements are constrained or imposed and which are not. This influence can be seen in all type of problems, ranging from simple beams to complicated structures. For tubular structures, such as flexible pipes and umbilical cables, the boundary conditions are usually given in terms of imposed movements in sections, which are commonly assumed, by hypothesis, as rigid bodies. To deal with this type of structures, the authors presented in previous works the macroelements. They are finite elements that incorporate geometrical characteristics in the formulation, leading to well behaved contact models with a smaller number of degrees of freedom. One major feature of the model is the orthotropic cylindrical layer that uses Fourier series for the displacements. This led to specific contact models and bring the difficulty in the representation of boundary conditions in terminal sections, since different nature displacements (one the aforementioned Fourier and other one standard description) must be dealt with. This paper address how to impose translational movement for sections using macroelements. All the description of how the coupling is made and the constraint enforcement done by using a penalty-based formulation. This work also highlights the implementation, finalizing with comparison with a conventional finite element program.

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