Penalty formulation of damage in classical composites

2006 ◽  
Author(s):  
P. Procházka ◽  
J. Matyáš
Keyword(s):  
Penalty Formulation

scholarly journals Dynamic Response Optimization of Complex Multibody Systems in a Penalty Formulation Using Adjoint Sensitivity

2015 ◽  
Vol 10 (3) ◽  
Author(s):  
Yitao Zhu ◽  
Daniel Dopico ◽  
Corina Sandu ◽  
Adrian Sandu
Keyword(s):  
Sensitivity Analysis ◽  
Multibody Dynamics ◽  
Multibody Systems ◽  
Real Life ◽  
Design Parameters ◽  
Vehicle Model ◽  
Adjoint Sensitivity ◽  
Penalty Formulation ◽  
Sensitivity Approach ◽  
Dynamic Performance Analysis

Multibody dynamics simulations are currently widely accepted as valuable means for dynamic performance analysis of mechanical systems. The evolution of theoretical and computational aspects of the multibody dynamics discipline makes it conducive these days for other types of applications, in addition to pure simulations. One very important such application is design optimization for multibody systems. In this paper, we focus on gradient-based optimization in order to find local minima. Gradients are calculated efficiently via adjoint sensitivity analysis techniques. Current approaches have limitations in terms of efficiently performing sensitivity analysis for complex systems with respect to multiple design parameters. To improve the state of the art, the adjoint sensitivity approach of multibody systems in the context of the penalty formulation is developed in this study. The new theory developed is then demonstrated on one academic case study, a five-bar mechanism, and on one real-life system, a 14 degree of freedom (DOF) vehicle model. The five-bar mechanism is used to validate the sensitivity approach derived in this paper. The full vehicle model is used to demonstrate the capability of the new approach developed to perform sensitivity analysis and optimization for large and complex multibody systems with respect to multiple design parameters with high efficiency.

Modeling Spatial Rigid Multibody Systems Using an Explicit-Time Integration Finite Element Solver and a Penalty Formulation

2004 ◽  
Author(s):  
Tamer Wasfy
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Time Integration ◽  
Rigid Bodies ◽  
Rotation Matrix ◽  
Explicit Time Integration ◽  
Penalty Formulation ◽  
A New Technique ◽  
Rigid Multibody

A new technique for modeling rigid bodies undergoing spatial motion using an explicit time-integration finite element code is presented. The key elements of the technique are: (a) use of the total rotation matrix relative to the inertial frame to measure the rotation of the rigid bodies; (b) time-integration of the rotational equations of motion in a body fixed (material) frame, with the resulting incremental rotations added to the total rotation matrix; (c) penalty formulation for creating connection points (virtual nodes which do not add extra degrees of freedom) on the rigid-body where joints can be placed. The use of the rotation matrix along with incremental rotation updates circumvents the problem of singularities associated with other types of three and four parameter rotation measures. Benchmark rigid multibody dynamics problems are solved to demonstrate the accuracy of the present technique.

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