• 한국소음진동공학회논문집
• /
• 제19권10호
• /
• pp.1069-1074
• /
• 2009

A sub-domain method for free vibration analysis of arbitrarily shaped, concave membranes with a deep groove is proposed in the paper. The proposed method divides the concave membrane of interest into two convex regions. The vibration displacement(approximate solution) of each convex region is assumed by linearly superposing plane waves generated at edges of the region. A sub-system matrix for each convex region is extracted by applying a provisional boundary condition to the approximate solution. Finally, a system matrix, which of the determinant gives eigenvalues of the concave membrane, is made by considering the fixed boundary condition(displacement zero condition) at edges and the compatibility condition(the condition of continuity in displacement and slope) at the interface between the two regions. Case studies show that the proposed method is valid and accurate when the eigenvalues by the proposed are compared to those by NDIF method, FEM, or the exact method.

• 소성∙가공
• /
• 제3권4호
• /
• pp.468-481
• /
• 1994

Mathematical description of arbitrarily-shaped tool surface are introduced by parametric patch approaches along with the related contact search algorithm. In order to maintain the advantages of membrane elements and to incoporate the bending effect, a BEAM(Bending Energy Augmented Membrane) element is proposed. Computation are carried out for some complex axisymmetric multi-stage deep drawing to verify the validity and the effectiveness of the proposed method.

• 한국자동차공학회논문집
• /
• 제4권6호
• /
• pp.27-38
• /
• 1996

A two-dimensional FEM program, which considers bending effects in the membrane fromulation, was developed under plane strain assumption for analyzing forming processes of an arbitrarily shaped draw-die of automotive panels. For the evaluation of bending effects with membrane elements, the bending equivalent forces and stiffnesses are calculated from the bending moment computed using the changes in curvature of the formed shape of two membrane ones. The curves depicted with 3 nodes are described by a circle, a quadratic equation, and a cubic equation, respectively, and in the simulation of the stretch/draw sections of an automotive inner panel, three different description results are compared each other. Also, the bending results are compared with membrane results and measurements in order to verify the validity of the developed program.

• 대한기계학회논문집A
• /
• 제22권3호
• /
• pp.493-503
• /
• 1998

The sectional forming analysis considering bending effects from the geometrically deformed shape of two linear membrane finite elements(called super element) was performed under plane strain assumption for analyzing forming processes of an arbitrarily shaped draw-die. For the evaluation of bending effects, the bending equivalent forces are calculated from the bending moment computed using the changes in the interior angle at the middle node of super element, and are agumented to the membrane stretch forces. In order to verify the validity of the bending formulation, the simulation results for the stretch, draw, and bend sections were compared with membrane analysis results and measurements.

• 대한기계학회논문집
• /
• 제15권1호
• /
• pp.169-178
• /
• 1991

본 연구에서는 평면 변형률 강소성 유한요소법을 이용하여 유한요소 수식화를 유도하고 금형이 해석저인 함수로 묘사되는 드로잉 공정을 해석하고, 금형이 해석적인 함수로 묘사되지 않는 실제적인 자동차 성형품의 드로잉 공정을 해석하여 기존의 결과 와 비교하여 본 방법의 타당성을 검토하였다.

• 소성∙가공
• /
• 제1권1호
• /
• pp.95-103
• /
• 1992

The plane strain analysis for simulating the stretch/draw forming operation with an arbitrarily-shaped tool profile is introduced. An implicit, incremental, updated Lagrangian formulation with a rigid-viscoplastic constitutive equation is employed. Contact and friction are considered through the mesh-normal, which compatibly describes arbitrary tool surfaces and FEM meshes without depending on the explicit spatial derivatives of tool surfaces. The linear line elements are used for depicting the formed sheet, based on membrane approximation. The FEM formulation is tested in the sections of automotive inner panel and two-side draw-in. Not only the excellent agreement between measured and computed strains is obtained in the stretched section, but also the numerical stability of formulation is verified in the draw-in section.

• Structural Engineering and Mechanics
• /
• 제13권4호
• /
• pp.437-453
• /
• 2002

In this paper, dynamic stiffness and flexibility for circular membranes are analytically derived using an efficient mixed-part dual boundary element method (BEM). We employ three approaches, the complex-valued BEM, the real-part and imaginary-part BEM, to determine the dynamic stiffness and flexibility. In the analytical formulation, the continuous system for a circular membrane is transformed into a discrete system with a circulant matrix. Based on the properties of the circulant, the analytical solutions for the dynamic stiffness and flexibility are derived. In deriving the stiffness and flexibility, the spurious resonance is cancelled out. Numerical aspects are discussed and emphasized. The problem of numerical instability due to division by zero is avoided by choosing additional constraints from the information of real and imaginary parts in the dual formulation. For the overdetermined system, the least squares method is considered to determine the dynamic stiffness and flexibility. A general purpose program has been developed to test several examples including circular and square cases.

• 오토저널
• /
• 제12권6호
• /
• pp.48-59
• /
• 1990

A finite element program was developed using line elements for simulating the stretch/draw forming operation of an arbitrarily-shaped plane-strain section. An implicit, incremental, updated Lagrangian formulation is employed, introducing a minimum plastic work path assumption for each time step. Geometric and material nonlinearities are also considered within each time step. The finite element equation is based on the mesh-normal, which compatibly describes arbitrary tool surfaces and FEM meshes without depending on the explicit spatial derivatives of tool surfaces. The membrane approximation is adopted under the plane stress assumption. The sheet material is assumed to obey a rigid-viscoplastic constitutive law. The developed program was tested in the die-tryout of typical automotive inner panels. In order to determine a single friction coefficient and boundary length, FEM results and measurements of thinning for a stretched section of final die were compared. After finding analysis parameters, the sheet forming operations of original and final die designs were simulated. Excellent agreement between measured and computed thickness strains was obtained and the developed program was able to identify die designs which were rejected during die tryout.

• 대한기계학회논문집
• /
• 제18권8호
• /
• pp.2113-2122
• /
• 1994

The 3-D FEM analysis for simulating the stamping operation of planar anisotropic sheet metals with arbitrarily-shaped tools is introduced. An implicit, incremental, updated Lagrangian formulation with a rigid-viscoplastic constitutive equation is employed. Contact and friction are considered through the mesh-normal, which compatibly describes arbitrary tool surfaces and FEM meshes without depending on the explicit spatial derivatives of tool surfaces. The consistent full set of governing relations, comprising equilibrium equation and mesh-normal geometric constraints, is appropriately linearized. The linear triangular elements are used for depicting the formed sheet, based on membrane approximation. Barlat's non-quadratic anisotropic yield criterion(strain-rate potential) is employed, whose in-plane anisotropic properties are taken into account with anisotropic coefficients and non-quadratic function parameter. The planar anisotropic finite element formulation is tested with the numerical simulations of the stamping of an automotive hood inner panel and the drawing of a hemispherical punch. The in-plane anisotropic effects on the formability of both mild steel and aluminum alloy sheet metals are examined.

• 한국정밀공학회지
• /
• 제29권1호
• /
• pp.114-120
• /
• 2012

We present a simple and low-cost method to fabricate poly(methyl-methacrylate) (PMMA) nanochannels with various shapes by combining the standard optical lithography with a PMMA layer transfer and collapse technique. We utilized PMMA membrane reflowing/collapsing phenomena into microchannels to fabricate nanochannels at both corners of arbitrarily-shaped microchannels. This allows nanochannels with various shapes such as curved nanochannels as well as straight nanochannels to be easily fabricated since the shape of the microchannel determines the shape of the nanochannels. This nanochannel fabrication method is simple, flexible, and low-cost since the standard optical lithography with low-resolution optical masks can be used to fabricate nanoscale channels as small as 100 nm wide with various shapes. Also, the sealing of nanochannels can be naturally achieved while the nanochannels are formed through the polymer layer transfer and collapse.