• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 1995.10a
• /
• pp.528-533
• /
• 1995

An analyical method is proposed to construct a clamp jointed structure as an equivalent stiffness matrix element in the finite element modal analysis of a complex beam structure. Static structural analysis was first made for the detail finite element model of the clamp joint. Utilizing the results of this analysis, the equivalent stiffness matrix element was buildup by using the flexibility influence coefficient method and Guyan condensation. The proposed method was applied to finite element modal analysis of a clamp jointed cantilever beam. And the finite element analysis results were compared to those experimental modal analysis. Comparison shows doog agreement each other Furthermore the effects of normal contact(or clamping) load on the equivalent stiffness matrix was also examined. The equivalent stiffness matrix showed little change in spite of the remakable increase in the contact load on the clamp joint.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.20 no.1
• /
• pp.88-99
• /
• 1996

The explicit scheme for finite element analysis of sheet metal forming problems has been widely used for providing practical solutions since it improves the convergency problem, memory size and computational time especially for the case of complicated geometry and large element number. The explicit schemes in general use are based on the elastic-plastic modeling of material requiring large computataion time. In the present work, a basic formulation for rigid-plastic explicit finite element analysis of plain strain sheet metal forming problems has been proposed. The effect of some basic parameters involved in the dynamic analysis has been studied in detail. Thus, the effective ranges of parameters have been proposed for numerical simultion by the rigid-plastic explicit finite element method. A direct trial-and-error method is introduced to treat contact and friction. In computation, sheet material is assumed to possess normal anisotropy and rigid-plastic workhardening characteristics. In order to show the validity and effectiveness of the proposed explicit scheme, computations are carried out for cylindrical punch stretching and the computational results are compared with those by the implicit scheme as well as with a commercial code. The proposed rigid-plastic exlicit finite element method can be used as a robust and efficient computational method for analysis of sheet metal forming.

• Journal of the Korean Society for Precision Engineering
• /
• v.17 no.4
• /
• pp.197-202
• /
• 2000

A simple numerical procedure is presented to determine the stress intensity factors for crack in a stiffened panel subjected to a uniaxial uniform stress normal to the crack. Two types of stiffened panels are analyzed by the finite element method for various values of crack lengths, stiffness ratios, and stiffener spacings. From the finite element solution, the stress intensity factors were determined by using hybrid extrapolation method. Results are presented in graphical forms for upper mentioned parameters.

• Journal of applied mathematics & informatics
• /
• v.8 no.3
• /
• pp.721-729
• /
• 2001

We consider finite element methods applied to a class of Sobolev equations in $R^d$($d{\geq}1$). Global strong superconvergence, which only requires that partitions are quais-uniform, is investigated for the error between the approximate solution and the Ritz-Sobolev projection of the exact solution. Two order superconvervgence results are demonstrated in $W^{1,p}({\Omega})$ and $L_p({\Omega})$ for $2{\leq}p$＜${\infty}$.

• Proceeding of KASS Symposium
• /
• 2006.05a
• /
• pp.256-264
• /
• 2006

This paper describes the formulation of rectangular flat shell element that is modeled with the six degree of freedoms including a rotational degree of freedom. The rectangular finite element matrix with a rotational degree of freedom is developed using a beam stiffness matrix and compared with other methods. The outputs of the quantity of vertical deflection of cantilever beam show us the improving evidence of the Frame-Shell finite element matrix in a calculation of vertical deflections of cantilever beam.

• Communications of the Korean Mathematical Society
• /
• v.10 no.3
• /
• pp.653-659
• /
• 1995

We prove that two essentially normal elements of a type $II_{\infty}$ factor von Neumann algebra are unitarily equivalent up to the compact ideal if and only if they have the identical essential spectrum and the same index data. Also we calculate the spectrum and essential spectrum of a non-unitary isometry of von Neumann algebra.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 1998.04a
• /
• pp.392-398
• /
• 1998

In order to check the validity of nonlinear normal modes of continuous, systems by means of the energy-based formulation, we consider a beam with a nonlinear boundary condition. The initial and boundary e c6nsl of a linear partial differential equation and a nonlinear boundary condition is reduced to a linear boundary value problem consisting of an 8th order ordinary differential equations and linear boundary conditions. After obtaining the asymptotic solution corresponding to each normal mode, we compare this with numerical results by the finite element method.

• Tunnel and Underground Space
• /
• v.10 no.2
• /
• pp.173-179
• /
• 2000

The influence of the plastic flow rules on the elasto-plastic behaviour of a discrete joint element was investigated by performing the numerical direct shear tests under both constant normal displacement and normal displacement conditions. The finite interface elements obeying Plesha’s joint constitutive law was used to allow the relative motion of the rock blocks on the joint surface. Realistic results were obtained in the tests adopting the non-associated flow rule, while the associated flow rule overestimated the joint dilation. To overcome the computational drawbacks coming from the non-symmetric element stiffness matrix in the conventional non-associated plasticity, the symmetric formulation of the tangential stiffness matrix for a non-associated joint element was proposed. The symmetric elasto-plastic matrix it derived by assuming an imaginary equivalent joint with associated flow rule which shows the same plastic response as that of original Joint with non-associated flow rule. The validity of the formulation was confirmed through the numerical direct shear tests under constant normal stress condition.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2007.04a
• /
• pp.577-582
• /
• 2007

A variational formulation for plane elasticity problems is derived based on an isogeometric approach. The isogeometric analysis is an emerging methodology such that the basis functions in analysis domain arc generated directly from NURBS (Non-Uniform Rational B-Splines) geometry. Thus. the solution space can be represented in terms of the same functions to represent the geometry. The coefficients of basis functions or the control variables play the role of degrees-of-freedom. Furthermore, due to h-. p-, and k-refinement schemes, the high order geometric features can be described exactly and easily without tedious re-meshing process. The isogeometric sensitivity analysis method enables us to analyze arbitrarily shaped structures without re-meshing. Also, it provides a precise construction method of finite element model to exactly represent geometry using B-spline base functions in CAD geometric modeling. To obtain precise shape sensitivity, the normal and curvature of boundary should be taken into account in the shape sensitivity expressions. However, in conventional finite element methods, the normal information is inaccurate and the curvature is generally missing due to the use of linear interpolation functions. A continuum-based adjoint sensitivity analysis method using the isogeometric approach is derived for the plane elasticity problems. The conventional shape optimization using the finite element method has some difficulties in the parameterization of boundary. In isogeometric analysis, however, the geometric properties arc already embedded in the B-spline shape functions and control points. The perturbation of control points in isogeometric analysis automatically results in shape changes. Using the conventional finite clement method, the inter-element continuity of the design space is not guaranteed so that the normal vector and curvature arc not accurate enough. On tile other hand, in isogeometric analysis, these values arc continuous over the whole design space so that accurate shape sensitivity can be obtained. Through numerical examples, the developed isogeometric sensitivity analysis method is verified to show excellent agreement with finite difference sensitivity.

• Computers and Concrete
• /
• v.28 no.5
• /
• pp.521-532
• /
• 2021

Present paper focuses on the modeling of size effect on the compressive strength of normal concrete with the application of Discrete Element Method (DEM). Test specimens with different size and shape were cast and uniaxial compressive strength test was performed on each sample. Five different concrete mixes were used, all belonging to a different normal strength concrete class (C20/25, C30/37, C35/45, C45/55, and C50/60). The numerical simulations were carried out by using the PFC 5 software, which applies rigid spheres and contacts between them to model the material. DEM modeling of size effect could be advantageous because the development of micro-cracks in the material can be observed and the failure mode can be visualized. The series of experiments were repeated with the model after calibration. The relationship of the parallel bond strength of the contacts and the laboratory compressive strength test was analyzed by aiming to determine a relation between the compressive strength and the bond strength of different sized models. An equation was derived based on Bazant's size effect law to estimate the parallel bond strength of differently sized specimens. The parameters of the equation were optimized based on measurement data using nonlinear least-squares method with SSE (sum of squared errors) objective function. The laboratory test results showed a good agreement with the literature data (compressive strength is decreasing with the increase of the size of the specimen regardless of the shape). The derived estimation models showed strong correlation with the measurement data. The results indicated that the size effect is stronger on concretes with lower strength class due to the higher level of inhomogeneity of the material. It was observed that size effect is more significant on cube specimens than on cylinder samples, which can be caused by the side ratios of the specimens and the size of the purely compressed zone. A limit value for the minimum size of DE model for cubes and cylinder was determined, above which the size effect on compressive strength can be neglected within the investigated size range. The relationship of model size (particle number) and computational time was analyzed and a method to decrease the computational time (number of iterations) of material genesis is proposed.