arXiv subjects

Myung-Jin Choi

Publications and source records attributed to Myung-Jin Choi.

6 recordsLinked to original sources

arXiv2026

A variable-offset joint formulation for beams with arbitrary cross-sections using a null space method

In this paper, we present a variational formulation of local configurational constraints that couple multiple beams with arbitrarily shaped cross-sections. Since this formulation requires no explicit interface to rotational degrees-of-freedom, it applies to any beam kinematics and finite element discretization. Here, we define the offset coordinates in a moving frame to constrain or release the relative position between connected beams. The present method is based on a first-order approximation of the Lagrange multiplier field in the cross-section, which limits the transferability of the joint to the resultant force and moment only. The multipliers are eliminated using a discrete null space method, which provides size reduction and improved conditioning of the system matrix. Further, we apply the developed formulation to a beam element based on extensible directors and to a brick element in nonlinear elastostatics. Several numerical examples are presented.

math.NA↗

arXiv2024

An objective isogeometric mixed finite element formulation for nonlinear elastodynamic beams with incompatible warping strains

We present a stable mixed isogeometric finite element formulation for geometrically and materially nonlinear beams in transient elastodynamics, where a Cosserat beam formulation with extensible directors is used. The extensible directors yield a linear configuration space incorporating constant in-plane cross-sectional strains. Higher-order (incompatible) strains are introduced to correct stiffness, whose additional degrees-of-freedom are eliminated by an element-wise condensation. Further, the present discretization of the initial director field leads to the objectivity of approximated strain measures, regardless of the degree of basis functions. For physical stress resultants and strains, we employ a global patch-wise approximation using B-spline basis functions, whose higher-order continuity enables to use much less degrees-of-freedom, compared to element-wise approximation. For time-stepping, we employ an implicit energy-momentum consistent scheme, which exhibits superior numerical stability in comparison to standard trapezoidal and mid-point rules. Several numerical examples are presented to verify the present method.

math.NA↗

arXiv2023

A selectively reduced degree basis for efficient mixed nonlinear isogeometric beam formulations with extensible directors

The effect of higher order continuity in the solution field by using NURBS basis function in isogeometric analysis (IGA) is investigated for an efficient mixed finite element formulation for elastostatic beams. It is based on the Hu-Washizu variational principle considering geometrical and material nonlinearities. Here we present a reduced degree of basis functions for the additional fields of the stress resultants and strains of the beam, which are allowed to be discontinuous across elements. This approach turns out to significantly improve the computational efficiency and the accuracy of the results. We consider a beam formulation with extensible directors, where cross-sectional strains are enriched to avoid Poisson locking by an enhanced assumed strain method. In numerical examples, we show the superior per degree-of-freedom accuracy of IGA over conventional finite element analysis, due to the higher order continuity in the displacement field. We further verify the efficient rotational coupling between beams, as well as the path-independence of the results.

math.NA↗

arXiv2022

An isogeometric finite element formulation for frictionless contact of Cosserat rods with unconstrained directors

This paper presents an isogeometric finite element formulation for nonlinear beams with impenetrability constraints, based on the kinematics of Cosserat rods with unconstrained directors. The beam cross-sectional deformation is represented by director vectors of an arbitrary order. For the frictionless lateral beam-to-beam contact, a surface-to-surface contact algorithm combined with an active set strategy and a penalty method is employed. The lateral boundary surface of the beam is parameterized by its axis and cross-sectional boundary curves with NURBS basis functions having at least $C^2$-continuity, which yields a continuous surface metric and curvature for the closest point projection. Three-dimensional constitutive laws of hyperelastic materials are considered. Several numerical examples verify the accuracy and efficiency of the proposed beam contact formulation in comparison to brick element solutions. The lateral contact pressure distribution of the beam formulation is in excellent agreement with the contact pressure of the brick element formulation while requiring much less degrees-of-freedom.

math.NA↗

arXiv2021

An isogeometric finite element formulation for geometrically exact Timoshenko beams with extensible directors

An isogeometric finite element formulation for geometrically and materially nonlinear Timoshenko beams is presented, which incorporates in-plane deformation of the cross-section described by two extensible director vectors. Since those directors belong to the space ${\Bbb R}^3$, a configuration can be additively updated. The developed formulation allows direct application of nonlinear three-dimensional constitutive equations without zero stress conditions. Especially, the significance of considering correct surface loads rather than applying an equivalent load directly on the central axis is investigated. Incompatible linear in-plane strain components for the cross-section have been added to alleviate Poisson locking by using an enhanced assumed strain (EAS) method. In various numerical examples exhibiting large deformations, the accuracy and efficiency of the presented beam formulation is assessed in comparison to brick elements. We particularly use hyperelastic materials of the St. Venant-Kirchhoff and compressible Neo-Hookean types.

physics.app-ph↗

arXiv2021

Isogeometric Configuration Design Optimization of Three-dimensional Curved Beam Structures for Maximal Fundamental Frequency

This paper presents a configuration design optimization method for three-dimensional curved beam built-up structures having maximized fundamental eigenfrequency. We develop the method of computation of design velocity field and optimal design of beam structures constrained on a curved surface, where both designs of the embedded beams and the curved surface are simultaneously varied during the optimal design process. A shear-deformable beam model is used in the response analyses of structural vibrations within an isogeometric framework using the NURBS basis functions. An analytical design sensitivity expression of repeated eigenvalues is derived. The developed method is demonstrated through several illustrative examples.

physics.app-ph↗