A mass matrix formulation for cohesive surface elements

Summary The stability and reflection‐transmission properties of the bipenalty method are studied in application to explicit finite element analysis of one‐dimensional contact‐impact problems. It is known that the standard penalty method, where an additional stiffness term corresponding to contact boundary conditions is applied, attacks the stability limit of finite element model. Generally, the critical time step size rapidly decreases with increasing penalty stiffness. Recent comprehensive studies have shown that the so‐called bipenalty technique, using mass penalty together with standard stiffness penalty, preserves the critical time step size associated to contact‐free bodies. In this paper, the influence of the penalty ratio (ratio of stiffness and mass penalty parameters) on stability and reflection‐transmission properties in one‐dimensional contact‐impact problems using the same material and mesh size for both domains is studied. The paper closes with numerical examples, which demonstrate the stability and reflection‐transmission behavior of the bipenalty method in one‐dimensional contact‐impact and wave propagation problems of homogeneous materials.

Section: Bipenalty Methodsmentioning

confidence: 99%

Section: Problem Description and Governing Equationsmentioning

confidence: 99%

On stability and reflection‐transmission analysis of the bipenalty method in contact‐impact problems: A one‐dimensional, homogeneous case study

Kopačka

Tkachuk

Gabriel

et al. 2017

“…[2][3][4][5][6] To alleviate the stepsize limitations imposed by the mesh frequencies whose response components contribute very little when low modes dominate the transient responses, various mass matrix tailoring have been introduced by altering the mass matrices to reduce/filter out the high frequencies of the dynamical system without affecting the low-mid frequencies. [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] Most of the existing methods cited above require either replacing existing elements by tailored elements and/or adopt element component-dependent time stepping procedures, leading to either elemental and/or global approaches, depending on how the modification of the mass matrix is made.…”

Section: Introductionmentioning

confidence: 99%

Large‐step explicit time integration via mass matrix tailoring

González

Park

2019

Summary A method for tailoring mass matrices that allows large time‐step explicit transient analysis is presented. It is shown that the accuracy of the present tailored mass matrix preserves the low‐frequency contents while effectively replacing the unwanted higher mesh frequencies by a user‐desired cutoff frequency. The proposed mass tailoring methods are applicable to elemental, substructural as well as global systems, requiring no modifications of finite element generation routines. It becomes most computationally attractive when used in conjunction with partitioned formulation as the number of higher (or lower) modes to be filtered out (or retained) are significantly reduced. Numerical experiments with the proposed method demonstrate that they are effective in filtering out higher modes in bars, beams, plain stress, and plate bending problems while preserving the dominant low‐frequency contents.

“…Recently, improvements of FEM mass matrices have been receiving an intense attention in the computational mechanics community. () The need for mass matrix improvements comes from 2 distinct motivations: efficient large explicit time integration step lengths for the analysis of highly nonlinear transient structural dynamics and dispersion accuracy improvements for wave propagation analysis. () The first one has been addressed by adopting lumped mass matrices that improves computational efficiency and at the same time decreases the highest frequency (often equalling to the highest mesh frequency).…”

Section: Introductionmentioning

confidence: 99%

Inverse mass matrix via the method of localized lagrange multipliers

González

Kolman

Cho

et al. 2017

Summary An efficient method for generating the mass matrix inverse of structural dynamic problems is presented, which can be tailored to improve the accuracy of target frequency ranges and/or wave contents. The present method bypasses the use of biorthogonal construction of a kernel inverse mass matrix that requires special procedures for boundary conditions and free edges or surfaces and constructs the free‐free inverse mass matrix using the standard FEM procedure. The various boundary conditions are realized by the the method of localized Lagrange multipliers. In particular, the present paper constructs the kernel inverse matrix by using the standard FEM elemental mass matrices. It is shown that the accuracy of the present inverse mass matrix is almost identical to that of a conventional consistent mass matrix or a combination of lumped and consistent mass matrices. Numerical experiments with the proposed inverse mass matrix are conducted to validate its effectiveness when applied to vibration analysis of bars, beams, and plain stress problems.