A simple finite element-based framework for the analysis of elastic pseudo-rigid bodies

Solberg, Jerome; Papadopoulos, Panayiotis

doi:10.1002/(sici)1097-0207(19990730)45:9<1297::aid-nme631>3.0.co;2-5

Cited by 26 publications

(17 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To be honest, some of them are also partially contained in Eringen's theory of micromorphic media, i.e., continua of infinitesimal affine bodies [8]. Later on, we developed the theory in various aspects [9,10,11,12,14,19,20,26,27,28,29,30,31,32,33,34,35,36,37,38,39,43] and some of our results were confirmed and developed by many people [15,16,17,21,22,40,41,42]. Let us also mention the papers like [3,4,5,6,18,44].…”

supporting

confidence: 62%

Constraints and symmetry in mechanics of affine motion

Gołubowska¹,

Kovalchuk²,

Sławianowski³

2014

Journal of Geometry and Physics

View full text Add to dashboard Cite

The aim of this paper is to perform a deeper geometric analysis of problems appearing in dynamics of affinely rigid bodies. First of all we present a geometric interpretation of the polar and two-polar decomposition of affine motion. Later on some additional constraints imposed on the affine motion are reviewed, both holonomic and non-holonomic. In particular, we concentrate on certain natural non-holonomic models of the rotation-less motion. We discuss both the usual d'Alembert model and the vakonomic dynamics. The resulting equations are quite different. It is not yet clear which model is practically better. In any case they both are different from the holonomic constraints defining the rotation-less motion as a time-dependent family of symmetric matrices of placements. The latter model seems to be non-geometric and non-physical. Nevertheless, there are certain relationships between our non-holonomic models and the polar decomposition.

show abstract

supporting

confidence: 62%

Constraints and symmetry in mechanics of affine motion

Gołubowska¹,

Kovalchuk²,

Sławianowski³

2014

Journal of Geometry and Physics

View full text Add to dashboard Cite

show abstract

“…For any affine mapping φ ∈ Aff(N, M ), an analogous representation is valid when the affine coordinates are fixed (i.e., origins of the reference frames and the linear bases) [7,10,19,20,[23][24][25][26][27][29][30][31][32][33][34][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][55][56][57][58]60]. Let us also quote the following 'representation' property of the operation L:…”

Section: Dynamics Of Affinely Rigid Bodiesmentioning

confidence: 99%

“…It can be shown that if ϕ is described in terms of the analytical expansion 52) and the velocity, i.e., the time derivative of (2.52) by:…”

Section: Dynamics Of Affinely Rigid Bodiesmentioning

confidence: 99%

Classical Dynamics of Fullerenes

Sławianowski

Kotowski

2017

Z. Angew. Math. Phys.

View full text Add to dashboard Cite

Abstract. The classical mechanics of large molecules and fullerenes is studied. The approach is based on the model of collective motion of these objects. The mixed Lagrangian (material) and Eulerian (space) description of motion is used. In particular, the Green and Cauchy deformation tensors are geometrically defined. The important issue is the group-theoretical approach to describing the affine deformations of the body. The Hamiltonian description of motion based on the Poisson brackets methodology is used. The Lagrange and Hamilton approaches allow us to formulate the mechanics in the canonical form. The method of discretization in analytical continuum theory and in classical dynamics of large molecules and fullerenes enable us to formulate their dynamics in terms of the polynomial expansions of configurations. Another approach is based on the theory of analytical functions and on their approximations by finite-order polynomials. We concentrate on the extremely simplified model of affine deformations or on their higher-order polynomial perturbations.Mathematics Subject Classification. 74H99.

show abstract

“…Here, we confine our attention to the theory with three directors. Our discussion of this theory is based on 2 As discussed in Rubin [8] and Solberg and Papadopoulos [12], the theories of Cosserat points and pseudo-rigid bodies can also be considered as a basis for the finite element method. Rubin [7] with some supplemental information from Cohen and Muncaster [11].…”

Section: Synopsis Of the Theory Of A Cosserat Pointmentioning

confidence: 99%