• Interaction and multiscale mechanics
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• 제6권2호
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• pp.107-125
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• 2013

A strain smoothing meshfree formulation with stabilized conforming nodal integration is presented for modeling the consolidation process in saturated porous media. In the present method, nodal strain smoothing is consistently introduced into the meshfree approximation of strain and pore pressure gradient variables associated with the saturated porous media. Meanwhile, in order to achieve a consistent numerical implementation, a smoothing approximation of the meshfree shape function within a nodal representative domain is also proposed in the stiffness construction. The resulting discrete system of equations is all expressed in smoothed nodal measures that are very efficient for numerical evaluation. Subsequently the space-time fully discrete equations are further established by the generalized trapezoidal rule for time integration. The effectiveness of the proposed meshfree consolidation analysis method is systematically illustrated by several benchmark problems.

• Journal of Advanced Marine Engineering and Technology
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• 제34권7호
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• pp.943-950
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• 2010

An efficient meshfree method based on a stabilized conforming nodal integration method is developed for elastoplastic contact analysis of metal forming processes. In this approach, strain smoothing stabilization is introduced to eliminate spatial instability in Galerkin meshfree methods when the weak form is integrated by a nodal integration. The gradient matrix associated with strain smoothing satisfies the integration constraint for linear exactness in the Galerkin approximation. Strain smoothing formulation and numerical procedures for path-dependent problems are introduced. Applications of metal forming analysis are presented, from which the computational efficiency has been improved significantly without loss of accuracy.

• Interaction and multiscale mechanics
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• 제1권3호
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• pp.339-355
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• 2008

A Galerkin meshfree method is presented for analyzing shear deformable cylindrical panels. Based upon the analogy between the cylindrical panel and the curved beam a pure bending mode for cylindrical panel is rationally constructed. The meshfree approximation employed herein is characterized by an enhanced moving least square or reproducing kernel basis function that can exactly represent the pure bending mode and thus meets the requirement of Kirchhoff mode reproducing condition. The variational form is discretized using the efficient stabilized conforming nodal integration with a smoothed nodal gradient based curvature. The resulting meshfree formulation satisfies the integration constraint for bending exactness. Moreover, it is shown here that the smoothed gradient preserves several desired properties which are valid for the standard gradient obtained by direct differentiation, such as partition of nullity and reproduction of a constant strain field. The efficacy of the proposed approach is demonstrated by two benchmark cylindrical panel examples.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2008년도 정기 학술대회
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• pp.172-176
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• 2008

In this paper, three dimensional linear conforming variable-finite elements are presented with the aid of a smoothed integration (a class of stabilized conforming nodal integration), for mnltiscale mechanics problems. These elements meet the desirable properties of an interpolation such as the Kronecker delta condition, the partition of unity condition and the positiveness of interpolation function. The necessary condition of linear exactness is fully relaxed by employing the smoothed integration, which renders us to meet the linear exactness in a straightforward manner. This novel element description extend the category of the conventional finite elements space to ration type function space and give the flexibility on the number of nodes of element which are fixed in the conventional finite elements. Several examples are provided to show the convergence and the accuracy of the proposed elements, and to demonstrate their potential with emphasis on the multiscale mechanics problems such as global/local analysis, nonmatching contact problems, and modeling of composite material with defects.

• 한국항공우주학회지
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• 제46권3호
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• pp.210-218
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• 2018

항공기와 같은 복잡한 구조물의 유한요소해석을 위해 자동요소망을 생성하면 일반적으로 삼각형 요소가 많이 생성되게 된다. 하지만 삼각형 요소는 사각형 요소에 비해 정확도가 떨어지므로 신뢰성 있는 해를 도출하기 어렵다. 이와 같은 문제는 배경셀 적분을 이용한 무요소법(Meshfree Method)을 통해 개선할 수 있으나 이 또한 적분점의 과다사용, 적분영역의 비효율성 등의 문제가 발생하게 된다. 이를 개선하기 위해 절점 기준으로 적분영역을 설정하여 적분을 수행하는 방법이 제안되었지만 비압축성 문제의 경우 해의 진동현상이 일어나는 등 수치 정확도가 떨어지게 된다. 따라서 본 연구에서는 적분영역을 절점영역이 아닌 요소영역으로 설정하는 수정된 무요소법을 통해 요소의 형태에 따른 정확도 저하가 발생되지 않고 기존의 무요소법에서 발생되는 수치 불안정성 등을 개선하였다. 2차원 예제를 통해 수정된 무요소법의 효용성을 검증하였다.