• Structural Engineering and Mechanics
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• v.18 no.6
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• pp.807-829
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• 2004

The Element-Based Lagrangian Formulation of a 9-node resultant-stress shell element is presented for the isotropic and anisotropic composite material. The effect of the coupling term between the bending strain and displacement has been investigated in the warping problem. The strains, stresses and constitutive equations based on the natural co-ordinate have been used throughout the Element-Based Lagrangian Formulation of the present shell element which offers an advantage of easy implementation compared with the traditional Lagrangian Formulation. The element is free of both membrane and shear locking behavior by using the assumed natural strain method such that the element performs very well in thin shell problems. In composite plates and shells, the transverse shear stiffness is defined by an equilibrium approach instead of using the shear correction factor. The arc-length control method is used to trace complex equilibrium paths in thin shell applications. Several numerical analyses are presented and discussed in order to investigate the capabilities of the present shell element. The results showed very good agreement compared with well-established formulations in the literature.

• Structural Engineering and Mechanics
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• v.18 no.2
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• pp.247-262
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• 2004

In the earlier application of the spline finite strip method(FSM), the uniform B3-spline functions were used in the longitudinal direction while the conventional interpolation functions were used in the transverse direction to construct the displacement filed in a strip. To overcome the shortcoming of the uniform B3-spline, non-periodic B-spline was developed as the displacement function. The use of non-periodic B3-spline function requires no tangential vectors at both ends to interpolate the geometry of shell and the Kronecker delta property is also satisfied at the end boundaries. Recently, non-periodic spline FSM which was modified to have a multiple knots at the boundary was developed for the shell analysis and applied to the analysis of bridges. In the formulation of a non-symmetric spline finite strip method, the concepts of non-periodic B3-spline and a stress-resultant finite strip with drilling degrees of freedom for a shell are used. The introduction of non-symmetrically spaced knots in the longitudinal direction allows the selective local refinement to improve the accuracy of solution at the connections or at the location of concentrated load. A number of numerical tests were performed to prove the accuracy and efficiency of the present study.

• Journal of the Korean Society for Advanced Composite Structures
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• v.3 no.2
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• pp.1-10
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• 2012

In the present study, an Element-Based Lagrangian Formulation for the nonlinear analysis of shell structures is presented. The strains, stresses and constitutive equations based on the natural co-ordinate have been used throughout the Element-Based Lagrangian Formulation of the present shell element which offers an advantage of easy implementation compared with the traditional Lagrangian Formulation. The Element-Based Lagrangian Formulation of a 9-node resultant-stress shell element is presented for the anisotropic composite material. The element is free of both membrane and shear locking behavior by using the assumed natural strain method such that the element performs very well in thin shell problems. The arc-length control method is used to trace complex equilibrium paths in thin shell applications. Numerical examples for laminated composite curved shells presented herein clearly show the validity of the present approach and the accuracy of the developed shell element.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.10a
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• pp.19-26
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• 1998

The isoparametric spline finite strip method for degenerated shells is presented. In the formulation, both the geometry and the displacement field are represented by uniform cubic B-spline curves. Spline shell strip is degenerated stress-resultant shell with 6 dof at each node;and the penalty function method is used to incorporated the six dof,

• Journal of Korean Society of Steel Construction
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• v.20 no.3
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• pp.409-419
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• 2008

A co-rotational quasi-conforming formulation of four- node stress resultant shell elements using Ivanov-Ilyushin yield criteria are presented for the nonlinear analysis of plate and shell structure. The formulation of the geometrical stiffness is defined by the full definition of the Green strain tensor and it is efficient for analyzing stability problems of moderately thick plates and shells as it incorporates the bending moment and transverse shear resultant force. As a result of the explicit integration of the tangent stiffness matrix, this formulation is computationally very efficient in incremental nonlinear analysis. This formulation also integrates the elasto-plastic material behaviour using Ivanov Ilyushin yield condition with isotropic strain hardening and its asocia ted flow rules. The Ivanov Ilyushin plasticity, which avoids multi-layer integration, is computationally efficient in large-scale modeling of elasto-plastic shell structures. The numerical examples herein illustrate a satisfactory concordance with test ed and published references.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.12 no.2
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• pp.185-199
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• 1999

본 연구에서는 새로운 spline 유한대판 요소를 제안하였다. 제안된 정식화는 등매개 개념에 의해 기하학적 형상과 변위장을 가정함에 있어 길이방향은 3차의 B-spline 곡선으로, 횡방향에 대해서는 Lagrange 다항식에 의해 표현된다. 이 논문은 평판과 쉘해석에 있어서의 등매개 spline 유한대판 요소의 개선에 목적을 두고 있다. 이 새로운 요소는 스트립의 내부 절점에서 6개의 자유도를 갖는 합-응력 감절점 쉘 요소로부터 유도하였다. 스트립의 기하학적 형상은 강체 회전에 대한 정의에 위배되지 않고도 두께 방향을 따라 Jacobian이 일정하다는 가정을 따랐으며 고체역학에서 정의되는 면내 회전을 penalty 함수에 의한 구속조건으로 간주하여 면내 회전에 관계된 자유도를 생성하였다. 제안된 요소에 대하여 쉘의 전형적인 문제에 대한 수치예제를 보였으며 이 스트립 요소의 성능을 평가하였다.

• Wind and Structures
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• v.34 no.3
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• pp.291-301
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• 2022

Although mostly used in wind turbine market, single rotor wind turbines have problems with transportation and installation costs due to their large size. In order to solve such problems, multi-rotor wind turbine is being proposed; however, light weight design of multi-rotor wind turbine is required considering the installation at offshore or deep sea. This study proposes the systematic design process of the multi-rotor wind turbine focused on its supporting structure with simultaneous consideration of static and dynamic behaviors in an ideal situation. 2D and successive 3D topology optimization process based on the density method were applied to minimize the compliance of supporting structure. To realize the conceptual design obtained by topology optimization for manufacturing feasibility, the derived 3D structure was modified to have shell structures and optimized again through parametric design using the design of experiments and the response surface method for detail design of their thicknesses and radii. The resultant structure was determined to satisfy the stress and the buckling load constraint as well as to minimize the weight and the resultant supporting structure were verified numerically.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1998.03a
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• pp.28-31
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• 1998

Wrinkling is one of the major defects in sheet metal products and may be also attributable to the wear of the tool. The initiation and growth of the wrinkles are influenced by many factors such as stress state, mechanical properites of the sheet material, geometry of the body, and contact condition. It is difficult to analyze the wrinkling initiation and growth considering the factors because the effects of the factors are very complex and the wrinkling behavior may show wide variation for small deviation of the factors. In this study, the bifurcation theory is introduced for the finite element analysis of wrinkling initiation and growth, All the above mentioned factors are conveniently considered by finite element method. The finite element formulation is based on the incremental deformation theory and elastic-plastic material modeling. The finite element analysis is carried out using the continuum-based resultant shell elements considering the planar anisotropy of the sheet metal. The proposed method is verified by employing to column buckling problem. And then, the initiation and growth of wrinkling in deep drawing of cylindrical cup are analyzed.