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Accuracy and Convergence Characteristics of Spring-Stiffness Formulations in the AEM for Laterally Loaded 2D Walls

횡력을 받는 2차원 벽체 해석을 위한 응용요소법 스프링 강성 정식화의 정확도와 수렴 특성

Dae-Jin Kim1*
,
Jonghwan Park2
김 대진1*
,
박 종환2
1Professor, Department of Architectural Engineering, Kyung Hee University, Yongin, 17104, Rep. of Korea
2PhD Student, Department of Architectural Engineering, Kyung Hee University, Yongin, 17104, Rep. of Korea
1경희대학교 건축공학과 교수
2경희대학교 건축공학과 박사과정
*Corresponding Author
31 July 2026. pp. 145-157
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Abstract

In the Applied Element Method (AEM) a continuum is represented by rigid elements connected with normal and shear springs, so the assigned spring stiffness governs the computed response; yet the literature and software manuals disagree on the shear stiffness by a factor of two (GA / L versus 2GA / L). This study evaluates four stiffness-setting strategies — GA / L, 2GA / L, the ELS shear-adjusted form, and patch-calibrated factors — for the linear-elastic static response of laterally loaded 2D walls against a converged plane-stress FEM reference and exact-solution patch tests. The GA / L family, including the manual’s shear-adjusted form, drifts away from the FEM solution under mesh refinement; its coarse-mesh agreement is a coincidental cancellation of discretization and formulation errors. Calibrated factors approach unity under refinement but do not transfer across deformation modes or element aspect ratios. The reliable route is mesh refinement with square elements and uncorrected kn = EA / L and ks = 2GA / L, which converges at O(h) toward a limit about 2 % stiffer than the continuum owing to the missing Poisson coupling.

Keywords
Applied element method
Spring stiffness
Shear spring
Patch test
2D wall

응용요소법(AEM)은 연속체를 강체 요소와 법선·전단 스프링으로 표현하므로 스프링 강성 설정이 해석 결과를 지배하지만, 전단 스프링 강성에 대해 문헌과 소프트웨어 매뉴얼은 GA / L과 2GA / L로 2배 엇갈린 식을 제시하고 있다. 본 연구는 횡력을 받는 2차원 벽체의 선형탄성 정적 응답을 대상으로 GA / L, 2GA / L, ELS shear-adjusted, 패치 보정 계수의 네 가지 강성 설정 전략을, 수렴 확인된 평면응력 FEM 기준해와 정해 패치 테스트에 대해 평가하였다. GA / L 계열은 매뉴얼의 shear-adjusted를 포함하여 격자를 세분화할수록 FEM 해에서 멀어졌으며, 거친 격자에서의 일치는 이산화 오차와 정식화 오차가 상쇄된 우연한 결과였다. 패치 보정 계수는 세분화와 함께 1.0에 접근하지만 변형 모드나 요소 종횡비가 달라지면 전이되지 않았다. 신뢰할 수 있는 경로는 정사각 요소에 보정 없는 kn = EA / L와 ks = 2GA / L를 적용하고 격자를 세분화하는 것으로, 이때 해는 Poisson 결합 부재로 인해 연속체 해보다 약 2 % 강성측인 극한을 향해 O(h)로 수렴한다.

키워드
응용요소법
스프링 강성
전단 스프링
패치 테스트
2차원 벽체
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Information
  • Publisher :Korea Protective Facility Institute
  • Publisher(Ko) :한국방호시설학회
  • Journal Title :Protective Facility
  • Journal Title(Ko) :방호시설
  • Volume : 3
  • No :3
  • Pages :145-157
  • Received Date : 2026-06-13
  • Revised Date : 2026-07-01
  • Accepted Date : 2026-07-08
  • DOI :https://doi.org/10.23310/PF.2026.3.3.145
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