• 한국소음진동공학회논문집
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• 제12권2호
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• pp.161-169
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• 2002

Based on the analytic expression for the elasto-dynamic behavior of rotating shaft, the transfer matrix is formulated for the shaft element with uniform cross-section. Timoshenko beam theory is Introduced for modeling the behavior of shaft. Complex variables representing the displacement, slope, moment and shear force are used for deriving the transfer matrix between both ends of the shaft element. Simulation result obtained by applying the transfer matrix to a general rotor model is compared with the reference result and proved to be exact. Natural frequencies and the corresponding modes are analyzed with varying the bearing: stiffness. The generally used bearings are considered for discussions. and the bearing stiffness is shown to affect the vibration characteristics of rotor.

• Structural Engineering and Mechanics
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• 제11권4호
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• pp.423-442
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• 2001

This paper presents a method of elastic-plastic analysis for planar steel frames that provides the accuracy of distributed plasticity methods with the computational efficiency that is greater than that of distributed plasticity methods but less than that of plastic-hinge based methods. This method accounts for the effect of spread of plasticity accurately without discretization through the cross-section of a beam-column element, which is achieved by the following procedures. First, nonlinear equations describing the relationships between generalized stresses and strains of the cross-section are derived analytically. Next, nonlinear force-deformation relationships for the beam-column element are obtained through lengthwise integration of the generalized strains. Elastic-plastic flexibility coefficients are then calculated by differentiating the above element force-deformation relationships. Finally, an elastic-plastic stiffness matrix is obtained by making use of the flexibility-stiffness transformation. Adding the conventional geometric stiffness matrix to the elastic-plastic stiffness matrix results in the tangent stiffness matrix, which can readily be used to evaluate the load carrying capacity of steel frames following standard nonlinear analysis procedures. The accuracy of the proposed method is verified by several examples that are sensitive to the effect of spread of plasticity.

• 대한기계학회논문집
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• 제18권10호
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• pp.2640-2652
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• 1994

The stiffness of 6-node isotropic element is stiffer than that of 8-node isotropic element of same configuration. This phenomenon was called 'Relative Stiffness Stiffening Phenomenon'. In this paper, an equation of sampling point modification which correct this phenomenon was derived for the composite plate, as well as an equation for an isotropic plate. The relative stiffness stiffening phenomena of an isotropic plate element could be corrected by modifying Gauss sampling points in the numerical integration of stiffness matrix. This technique could also be successfully applied to the static analyses of composite plate modeled by the 3-dimensional 16-node elements. We predicted theoretical errors of stiffness versus the number of layers that result from the reduction of numerical integration order. These errors coincide very well with the actual errors of stiffness. Therefore, we can choose full integration of reduced integration based upon the permissible error criterion and the number of layers by using the thoretically predicted error.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2006년도 정기 학술대회 논문집
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• pp.589-596
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• 2006

An improved numerical method to obtain the exact element stiffness matrix is newly proposed to perform the spatially coupled elastic and stability analyses of non-symmetric thin-walled beam-columns with two-types of elastic foundation. This method overcomes drawbacks of the previous method to evaluate the exact stiffness matrix for the spatially coupled stability analysis of thin-walled beam-column. This numerical technique is firstly accomplished via a generalized eigenproblem associated with 14 displacement parameters by transforming equilibrium equations to a set of first order simultaneous ordinary differential equations. Then exact displacement functions are constructed by combining eigensolutions and polynomial solutions corresponding to non-zero and zero eigenvalues, respectively. Consequently an exact stiffness matrix is evaluated by applying the member force-deformation relationships to these displacement functions.

• Korean Journal of Mathematics
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• 제6권1호
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• pp.17-26
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• 1998

In this paper, we briefly study the condition number of stiffness matrix with $h$-version and analyze it with $p$-version of the finite element method.

• Structural Engineering and Mechanics
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• 제35권6호
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• pp.717-733
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• 2010

The dynamic stiffness matrix is formulated for an axially loaded slender double-beam element in which both beams are homogeneous, prismatic and of the same length by directly solving the governing differential equations of motion of the double-beam element. The Bernoulli-Euler beam theory is used to define the dynamic behaviors of the beams and the effects of the mass of springs and axial force are taken into account in the formulation. The dynamic stiffness method is used for calculation of the exact natural frequencies and mode shapes of the double-beam systems. Numerical results are given for a particular example of axially loaded double-beam system under a variety of boundary conditions, and the exact numerical solutions are shown for the natural frequencies and normal mode shapes. The effects of the axial force and boundary conditions are extensively discussed.

• 한국공간구조학회논문집
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• 제3권2호
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• pp.85-90
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• 2003

If we use a third order approximation for the displacement function of beam element in finite element methods, finite element solutions of beams yield nodal displacement values matching to beam theory results to have no connection with the number increasing of elements of beams. It is assumed that, as the member displacement value at beam nodes are correct, the calculation procedure of beam element stiffness matrix have no numerical errors. A the member forces are calculated by the equations of $\frac{-M}{EI}=\frac{{d^2}{\omega}}{dx^2}\;and\;\frac{dM}{dx}=V$, the member forces at nodes of beams have errors in a moment and a shear magnitudes in the case of smaller number of element. The nodal displacement value of plate subject to the lateral load converge to the exact values according to the increase of the number of the element. So it is assumed that the procedures of plate element stiffness matrix calculations has a error in the fundamental assumptions. The beam methods for the high accuracy ratio solution Is also applied to the plate analysis. The method of reducing a error ratio of member forces and element stiffness matrix in the finite element methods is studied. Results of study were as follows. 1. The matrixes of EI[B] and [K] in the equations of M(x)=EI[B]{q} and M(x) = [K]{q}+{Q} of beams are same. 2. The equations of $\frac{-M}{EI}=\frac{{d^2}{\omega}}{dx^2}\;and\;\frac{dM}{dx}=V$ for the member forces have a error ratio in a finite element method of uniformly loaded structures, so equilibrium node loads {Q} must be substituted in the equation of member forces as the numerical examples of this paper revealed.

• 한국정밀공학회지
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• 제14권8호
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• pp.137-145
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• 1997

A two-dimensional program for the analysis of bimaterial inclusion has been developed using the bound- ary element method. In order to study the effects of circular inclusion on the stress field of the crack tip, numerical analysis was performed for the straight crack of finite length around the symmetric circular inclusion whose modulus of elasticity was different from that of the matrix material. In the case of inclusion whose stiffness was smaller than that of the matrix material, the stress intensity factor was found to increase as the crack enamated. The stress intensity factor was uninfluenced from the radial change in inclusion and remained constant for the stiffness equivalent to the matrix materials, where as it decreased for the inclusion with larger stiffness. For the vareation in the distance of the inclusion, a small increase in the stress intensity factor was observed for the case with small or equal stiffness compared with the matrix materials. The inclusion with larger stiffness showed a gradual decrease in the strss intensity factor as the crack emanated.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2000년도 가을 학술발표회논문집
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• pp.369-376
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• 2000

For the general loading condition and boundary condition, it is very difficult to obtain closed-form solutions for buckling loads and natural frequencies of thin-walled structures because its behaviour is very complex due to the coupling effect of bending and torsional behaviour. Consequently most of previous finite element formulations introduced approximate displacement fields using shape functions as Hermitian polynomials, isoparametric interpoation function, and so on. The purpose of this study is to calculate the exact displacement field of a thin-walled straight beam element with the non-symmetric cross section and present a consistent derivation of the exact dynamic stiffness matrix. An exact dynamic element stiffness matrix is established from Vlasov's coupled differential equations for a uniform beam element of non-symmetric thin-walled cross section. This numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. The natural frequencies are evaluated for the non-symmetric thin-walled straight beam structure, and the results are compared with available solutions in order to verify validity and accuracy of the proposed procedures.

• 대한기계학회논문집A
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• 제20권4호
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• pp.1225-1232
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• 1996

In this paper the vibration and power flow analysis for the branched piping system conveying fluid are performed by wave approach. The uniform straight pipe element conveying fluid is formulated using the dynamic stiffness matrix by wave approach. The branched piping system conveying fluid can be easily formulated with considering of simple assumptions of displacements at the junction and continuity conditions of the pipe internal flow. The dynamic stiffness matrix for each uniform straight pipe element can be assembled by using the global assembly technique using in conventional finite element method. The computational method proposed in this paper can easily calculate the forced responses and power flow of the branched piping system conveying fluid regardless of finite element size and modal properties.