Nonlinear Structure of Co-rotational and Intrinsic Beam Theories from a Variational Projection Perspective

Jun-Sik Kim

doi:10.7734/COSEIK.2026.39.4.219

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2026 Vol.39, Issue 4 Preview Page Next Page

Nonlinear Structure of Co-rotational and Intrinsic Beam Theories from a Variational Projection Perspective 변분 사영 관점에서 본 공회전 및 내재적 보 이론의 비선형 구조

31 August 2026. pp. 219-228

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Abstract

This paper reinterprets the nonlinear geometric structure of beam theory from a variational projection perspective and establishes the structural relationship between the co-rotational (CR) formulation and intrinsic (strain-based) beam theory. Although these two approaches have traditionally been developed independently, they are unified here within a common geometric framework based on the same underlying continuum. The analysis distinguishes between intrinsic nonlinear components shared by both formulations and differences resulting from coordinate representation. In particular, the coupling between torsion and axial force is identified as a fundamental geometric structure. Using this unified interpretation, a co-rotational frame-based local nonlinear beam model is developed using a variational perturbation approach, and a systematic procedure for computing cross-sectional perturbations is presented. The proposed framework combines the computational efficiency of the co-rotational formulation with the geometric consistency of the intrinsic approach, providing a unified basis for nonlinear beam analysis.

Keywords

variational projection

co-rotational formulation

intrinsic beam theory

nonlinear mechanics

본 논문은 보 이론의 비선형 기하학적 구조를 변분 사영 관점에서 재해석하고, 공회전(CR) 정식화와 내재적(intrinsic) 보 이론 간의 구조적 관계를 규명한다. 두 접근법은 기존에 독립적으로 발전해 왔으나, 본 연구는 이를 동일한 연속체 기반의 공통 기하학 구조로 통합한다. 분석 결과, 곡률 벡터와 단면 위치의 결합으로부터 유도되는 비틀림-축력 결합 항은 좌표계 선택과 무관한 내재적 구조임을 확인하였으며, 이를 두 정식화를 관통하는 핵심 기하학 성분으로 규명한다. 한편 일부 비선형 항은 변수 선택과 사영 방식에 따라 표현 형태가 달라질 뿐으로, 두 이론의 차이는 본질이 아닌 표현의 차이에 기인함을 밝힌다. 이러한 통합적 해석을 바탕으로, 변분 섭동법을 적용한 공회전 좌표계 기반의 국소 비선형 보 모델을 구성하고, 단면 섭동 변위를 체계적으로 계산하는 방법을 제시한다. 제안된 정식화는 와그너 효과와 블라소프 비틀림을 별도의 가정이나 보정없이 자연스럽게 포함하며, 이를 통해 공회전 정식화의 계산 효율성과 내재적 정식화의 기하학적 일관성을 결합한 통합적 해석 틀을 제공한다.

키워드

변분 사영

공회전 정식화

내재적 보 이론

비선형 역학

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Information

Publisher :Computational Structural Engineering Institute of Korea
Publisher(Ko) :한국전산구조공학회
Journal Title :Journal of the Computational Structural Engineering Institute of Korea
Journal Title(Ko) :한국전산구조공학회 논문집
Volume : 39
No :4
Pages :219-228
Received Date : 2026-05-11
Revised Date : 2026-06-08
Accepted Date : 2026-06-09
DOI :https://doi.org/10.7734/COSEIK.2026.39.4.219

Journal of the Computational Structural Engineering Institute of Korea ISSN:1229-3059(Print) 2287-2302(Online) 한국전산구조공학회 논문집

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