Isogeometric contact analysis using mortar method

Abstract

SUMMARYIn the present work, an isogeometric contact analysis scheme using mortar method is proposed. Because the isogeometric analysis is employed for contact analysis, the geometric exactness of the contact region is maintained without any loss of geometric data because of geometry approximation. Thus, the proposed method can overcome underlying shortcomings that result from the geometric approximation of contact surfaces in the conventional finite element (FE)-based contact analysis. For an isogeometric contact analysis, the schemes for treating the contact conditions and detecting the real contact surfaces are essentially required. In the proposed method, the mortar method is adopted as a nonconforming contact treatment scheme because it is expected to be in good harmony with the useful characteristics of nonuniform rational B-spline A new matching algorithm is proposed to combine the mortar method with the isogeometric analysis to guarantee consistent contact surface information with the nonuniform rational B-spline curve. The present scheme is verified by patch test and the well-known problems which have theoretical solutions such as interference fit and the Hertzian contact problem. It is shown that the problems with curved contact surfaces which are difficult to treat by conventional approaches can be easily dealt with.

Isogeometric dual mortar methods for computational contact mechanics

“…For contact algorithms based on Lagrangian finite elements such methods can be found in e.g. [36,[41][42][43][44] and within IGA in [12,13]. Using these methods based on a standard Lagrange multiplier interpolation, a system of increased size containing both displacement and Lagrange multiplier degrees of freedom has to be solved.…”

“…As a consequence, in the past five years various discretization techniques have been developed for IGA or transferred from finite element based contact mechanics to IGA, such as node-to-segment [4], Gauss-point-to-segment [5][6][7][8][9][10] and mortar methods [5,6,[11][12][13][14]. We refer to the recent review in [15] for a comprehensive discussion of such methods, comparisons to their finite element counterparts and further references.…”

“…While Gauss-point-to-segment approaches are, due to their lack of inf-sup stability (see e.g. [5,7] for numerical investigations), usually combined with a penalty approach, see [7][8][9][10], node-to-segment and mortar formulations can be combined with penalty methods [5,6], Uzawa-type algorithms [11], Lagrange multiplier methods [13,14] or augmented Lagrange methods [12]. In contrast to penalty methods, the other mentioned methods fulfill the contact constraints in a discrete sense exactly.…”

Isogeometric contact: a review

“…The simplicity of this approach goes at the expenses of the robustness, especially for large sliding cases or for cases where the slave surface is in intermittent or partial contact. A partial improvement was proposed by Kim and Youn (2012) in the 2D setting. In their approach, each slave surface element in partial contact is divided through knot insertion into its active and inactive portions, and an iterative procedure based on the bisection method is used to identify the boundary of the active region.…”

A gap element for treating non-matching discrete interfaces

“…These corrective strategies either can lead to ill-conditioning of the constraint equations and or nonlinear mapping algorithms [19,20]. Isogeometry elements have been proposed to alleviate the complications associated with interface gaps [21,22]. However, while theoretically plausible, enormous implementation complexities and corrective measures need to be overcome for isogeometry interface treatment procedures before it can be used in a routine manner, especially for cases involving threedimensional CAD-generated interface geometries (see, e.g., a recent review article [23]).…”