An M(M-1K)m proportional damping in explicit integration of dynamic structural systems

Abstract

Algorithmic aspects of energy dissipation mechanisms of dynamic structural systems in conjunction with central di erence time integration method are investigated and damping proportional to

A computationally efficient numerical model for a dynamic analysis of thin plates based on the combined finite–discrete element method

“…where E is the modulus of elasticity, v is the Poisson ratio, Ê d is the shape changing part and Ê s is the volume changing part of the Green-St. Venant strain tensor, l is the damping coefficient and D is the rate of the deformation tensor [18,27]. Equivalent nodal forces are integrated directly from traction forces along the edges of the finite element:…”

“…This paper presents the discretization of the problem, with a description of the membrane and transverse carrying mechanism of the finite elements. The algorithms are implemented into the open source FDEM package 'Yfdem' [18,22,[24][25][26][27]. In addition, numerical examples are presented and discussed, illustrating the accuracy of the proposed numerical model.…”

A combined implicit–explicit algorithm in time for non‐linear finite element analysis

“…Mass matrix proportional damping is used [9] C = M. In addition, Munjiza's proposal [10], which includes sti ness and mass relationship to obtain damping, has been used in the analysis that requires to damp a wide range of frequencies…”

“…The divergence criterion (to give up IMP) is based upon the relative residual norm, expression (10). Upon failure of convergence within an incremental loading step, the last converged iteration at IMP corresponding to solution to the previous external loading step (displacementũ) is transferred to EXP as an initial condition.…”

A Comparison of Large Deflection Analysis of Bending Plates by Dynamic Relaxation

“…Munjiza et al supposed that damping is proportional to the power of the mass and stiffness matrices. They showed that when the damping matrix is 2M(M −1 S ) 0.5 , all modes will be critically damped [36,37].…”