• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1993년도 봄 학술발표회논문집
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• pp.11-18
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• 1993

An Analytical study of shear locking is introduced for linear thick beam element. The appropriate sampling point which eliminate shear locking phenomenon was Proposed through this study. Reduced integration point is exactly same as the sampling point obtained from this study. Numerical example indicates how shear locking is serious. some solutions for shear locking are presented.

• 한국공작기계학회논문집
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• 제12권5호
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• pp.73-79
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• 2003

In this paper, RKPM is extended for solving moderately thick and thin beams. General Timoshenko beam theory is used for formulation. Shear locking is the main difficulty in analysis of these kinds of structures. Shear relaxation factor, which is formulated using the difference between bending and shear strain energy, and corrected shear rigidity are introduced to overcome shear locking. Analysis results obtained reveal that RKPM using introduced methods is free of locking and very effectively applicable to deep beams as well as shallow beams.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 춘계학술대회논문집A
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• pp.680-685
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• 2001

In this paper, RKPM is extended for solving moderately thick and thin structures. General Timoshenko beam and Mindlin plate theory are used far formulation. Shear locking is the main difficulty in analysis of these kinds of structures. Shear relaxation factor, which is formulated using the difference between bending and shear strain energy, is introduced to overcome shear locking. Analysis results obtained reveal that RKPM using introduced method is free of locking and very effectively applicable to deeply as well as shallowly beams and plates.

• Structural Engineering and Mechanics
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• 제50권2호
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• pp.181-199
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• 2014

Locking phenomenon is a mesh problem and can be staved off with mesh refinement. If the studier is not preferred going to the solution with increasing mesh size or the computer memory can stack over flow than using higher order plate finite element or using integration techniques is a solution for this problem. The purpose of this paper is to show the shear locking phenomenon can be avoided by increase low order finite element mesh size of the plates and to study shear locking-free analysis of thick plates using Mindlin's theory by using higher order displacement shape function and to determine the effects of various parameters such as the thickness/span ratio, mesh size on the linear responses of thick plates subjected to uniformly distributed loads. A computer program using finite element method is coded in C++ to analyze the plates clamped or simply supported along all four edges. In the analysis, 4-, 8- and 17-noded quadrilateral finite elements are used. It is concluded that 17-noded finite element converges to exact results much faster than 8-noded finite element, and that it is better to use 17-noded finite element for shear-locking free analysis of plates.

• 대한토목학회논문집
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• 제11권3호
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• pp.1-10
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• 1991

본 논문에서는 개선된 감절점(degenerated) 쉘 유한요소의 복합적충을 갖는 쉘구조에의 적용성을 고찰하였다. 본 논문의 개선된 쉘 요소는 shear locking 해결에 우수한 결과를 보인 가정된 전단변형도를 대치사용하고, membrane locking 현상을 제거하기 위해 평면내 변형도의 구성시 감차적분을 행하며, 쉘요소 자체의 거동을 보완하기 위해 비적합변위형을 선택적으로 추가하였다. 본 요소는 shear/membrane locking이 발생하지 않으며, 전달가능한 거짓 영에너지모드도 나타나지 않는다. 유한변형을 고려한 기하학적 비선형 방정식을 total Lagrangian 수식화를 시용하여 정형화 하였고, 비선형 수치해석은 Newton-Raphson 반복법으로 반복 계산한다. 여러 예제해석을 통하여 본 개선된 쉘 유한요소의 유용성과 정확도를 고찰하였다.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2002년도 봄 학술발표회 논문집
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• pp.35-42
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• 2002

In this paper, effective analysis of beam is studied using the RKPM in meshless methods. So, RKPM is extended for solving moderately thick and thin beam. General Timoshenko beam theory is used for formulation. Shear locking is the main difficulty in analysis of beam structures. The shear relaxation factor and corrected shear rigidity are introduced to overcome shear locking. Analysis results obtained reveal that RKPM using introduced methods Is free of locking and very effectively applicable to deeply as well as shallowly beams.

• Structural Engineering and Mechanics
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• 제11권2호
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• pp.123-132
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• 2001

An improved version of the Element-free Galerkin method (EFGM) is presented here for addressing the problem of transverse shear locking in shear-deformable beams with a high length over thickness ratio. Based upon Timoshenko's theory of thick beams, it has been recognized that shear locking will be completely eliminated if the rotation field is constructed to match the field of slope, given by the first derivative of displacement. This criterion is applied directly to the most commonly implemented version of EFGM. However in the numerical process to integrate strain energy, the second derivative of the standard Moving Least Square (MLS) shape functions must be evaluated, thus requiring at least a $C^1$ continuity of MLS shape functions instead of $C^0$ continuity in the conventional EFGM. Yet this hindrance is overcome effortlessly by only using at least a $C^1$ weight function. One-dimensional quartic spline weight function with $C^2$ continuity is therefore adopted for this purpose. Various numerical results in this work indicate that the modified version of the EFGM does not exhibit transverse shear locking, reduces stress oscillations, produces fast convergence, and provides a surprisingly high degree of accuracy even with coarse domain discretizations.

• Structural Engineering and Mechanics
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• 제40권3호
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• pp.393-410
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• 2011

The eight-node 3D solid element is one of the most extensively used elements in computational mechanics. This is due to its simple shape and easy of discretization. However, due to the parasitic shear locking, it should not be used to simulate the behaviour of structural members in bending dominant conditions. Previous researches have indicated that the introduction of incompatible mode into the displacement field of the solid element could significantly reduce the shear locking phenomenon. In this study, an incompatible mode eight-node solid element, which considers both geometric and material nonlinearities, is developed for modelling of structural members at elevated temperatures. An algorithm is developed to extend the state determination procedure at ambient temperature to elevated temperatures overcoming initially converged stress locking when the external load is kept constant. Numerical studies show that this incompatible element is superior in terms of convergence, mesh insensitivity and reducing shear locking. It is also showed that the solid element model developed in this paper can be used to model structural behaviour at both ambient and elevated temperatures.

• Structural Engineering and Mechanics
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• 제5권6호
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• pp.853-865
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• 1997

The design of robust plate and shell elements has been a very challenging area for several decades. The main difficulty has been the shear locking phenomenon in plate elements and the shear and membrane locking phenomena together in the shell elements. Among the various artifices or devices which are used to develop elements free of these problems is the field-consistency approach. In this paper this approach is reviewed, It turns out that not only Mindlin type elements but also elements based on higher-order theories could be developed using the technique.

• Structural Engineering and Mechanics
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• 제2권1호
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• pp.17-34
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• 1994

This paper proposes a new four node degenerated shell element. In the formulation of the new element, the assumed covariant shear strains are used to avoid the shear locking problem, and the assumed covariant membrane strains are applied to alleviate the membrane locking problem and also to improve the membrane bending performance. The assumed covariant strains are obtained from the covariant strain field defined with respect to the element natural coordinate system. This formulation enables us to obtain a shell element, which does not produce spurious singular modes, avoids locking phenomena, and excels in calculation efficiency. Several examples in this paper indicate that, despite its simplicity, the achieved accuracy and convergence are satisfactory.