• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제25권4호
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• pp.262-295
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• 2021

This paper introduces mono-implicit general linear methods, a special class of general linear methods, which are implicit in the output solution for the numerical integration of differential algebraic equations. We show how L-stable inherent Runge-Kutta members can be derived. The procedures for implementation have been discussed. The numerical test on the problem considered shows that the methods have improved accuracy when compared to RADAU IIA and the results from MATLAB ode15s, which have been taken as our reference solution.

• Structural Engineering and Mechanics
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• 제28권2호
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• pp.221-238
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• 2008

Numerical solution to buckling analysis of beams and columns are obtained by the method of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for various support conditions considering the variation of flexural rigidity. The solution technique is applied to find the buckling load of fully or partially embedded columns such as piles. A simple semi- inverse method of DQ or HDQ is proposed for determining the flexural rigidities at various sections of non-prismatic column ( pile) partially and fully embedded given the buckling load, buckled shape and sub-grade reaction of the soil. The obtained results are compared with the existing solutions available from other numerical methods and analytical results. In addition, this paper also uses a recently developed technique, known as the differential transformation (DT) to determine the critical buckling load of fully or partially supported heavy prismatic piles as well as fully supported non-prismatic piles. In solving the problem, governing differential equation is converted to algebraic equations using differential transformation methods (DT) which must be solved together with applied boundary conditions. The symbolic programming package, Mathematica is ideally suitable to solve such recursive equations by considering fairly large number of terms.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국내학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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• pp.926-930
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• 1993

An efficient method of formulating the equations of motion of multibody systems is presented. The equations of motion for each body are formulated by using Newton-Eulerian approach in their generic form. And then a transformation matrix which relates the global coordinates and relative coordinates is introduced to rewrite the equations of motion in terms of relative coordinates. When appropriate set of kinematic constraints equations in terms of relative coordinates is provided, the resulting differential and algebraic equations are obtained in a suitable form for computer implementation. The system geometry or topology is effectively described by using the path matrix and reference body operator.

• Steel and Composite Structures
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• 제35권5호
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• pp.671-685
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• 2020

This manuscript presents impacts of gradation of material functions and axial load functions on critical buckling loads and mode shapes of functionally graded (FG) thin and thick beams by using higher order shear deformation theory, for the first time. Volume fractions of metal and ceramic materials are assumed to be distributed through a beam thickness by both sigmoid law and symmetric power functions. Ceramic-metal-ceramic (CMC) and metal-ceramic-metal (MCM) symmetric distributions are proposed relative to mid-plane of the beam structure. The axial compressive load is depicted by constant, linear, and parabolic continuous functions through the axial direction. The equilibrium governing equations are derived by using Hamilton's principles. Numerical differential quadrature method (DQM) is developed to discretize the spatial domain and covert the governing variable coefficients differential equations and boundary conditions to system of algebraic equations. Algebraic equations are formed as a generalized matrix eigenvalue problem, that will be solved to get eigenvalues (buckling loads) and eigenvectors (mode shapes). The proposed model is verified with respectable published work. Numerical results depict influences of gradation function, gradation parameter, axial load function, slenderness ratio and boundary conditions on critical buckling loads and mode-shapes of FG beam structure. It is found that gradation types have different effects on the critical buckling. The proposed model can be effective in analysis and design of structure beam element subject to distributed axial compressive load, such as, spacecraft, nuclear structure, and naval structure.

• Journal of Mechanical Science and Technology
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• 제19권spc1호
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• pp.461-472
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• 2005

A formulation for flexible multibody systems (MBS) is investigated, where rigid MBS substructures are coupled with flexible bodies described by a nonlinear finite element (FE) approach. Several aspects that turned out to be crucial for the presented approach are discussed. The system describing equations are given in differential algebraic form (DAE), where many sophisticated solvers exist. In this paper the performance of several solvers is investigated regarding their suitability for the application to the usually highly stiff DAE. The substructures are connected with each other by nonlinear algebraic constraint equations. Further, partial derivatives of the constraints are required, which often leads to extensive algebraic trans-formations. Handcoding of analytically determined derivatives is compared to an approach utilizing algorithmic differentiation.

• 한국항공우주학회지
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• 제30권3호
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• pp.8-16
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• 2002

헬리콥터 비행 시뮬레이션을 위한 로터 운동방정식을 implicit formulation 형태로 유도하였다. 좌표계 사이의 상대운동을 고려한 일반화된 벡터 kinematics 를 유도하고 이를 적용하여 브레이드 임의 위치 에서 관성속도 및 관성가속도를 구하였다. 유도된 속도 및 가속도 벡터를 이용하여 플래핑, 리드래그 및 토오크 방정식 등을 implicit form으로 유도하였다. 브레이드 스팬에 따른 공간 적분 방법을 살펴보고, 다양한 힌지형상 및 힌지배열 순서에 관계없이 응용영역을 확장할 수 있음을 밝혔다. DAE(Differential Algebraic Equation) 형태를 갖는 본 연구의 결과식을 이용하여 동특성 계산을 위한 시간적분법을 검토하였다.

• Structural Engineering and Mechanics
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• 제43권1호
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• pp.105-126
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• 2012

Based on the first-order shear deformation theory (FSDT), and the virtual work principle, an elastic analysis for axisymmetric clamped-clamped Pressurized thick truncated conical shells made of functionally graded materials have been performed. The governing equations are a system of nonhomogeneous ordinary differential equations with variable coefficients. Using the matched asymptotic method (MAM) of the perturbation theory, these equations could be converted into a system of algebraic equations with variable coefficients and two systems of differential equations with constant coefficients. For different FGM conical angles, displacements and stresses along the radius and length have been calculated and plotted.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1992년도 추계학술대회 논문집
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• pp.349-353
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• 1992

The purpose of this paper is to develop methods for the dynamic analysis of multibody system that consist of interconnected rigid and deformable component. The equations of motion are derived by using the Lagrange's equation and finite element theory for the elastic mechanism systems. The type of equation of motion is the differential algebraic equation included kinematic nonlinear algebraic equation. The generalized coordinate partitioning method is used for solving this equation. To show the validity of this analysis solver, couple of models were canalized and those results were compared with the commercial package(ADAMS).

• 전기학회논문지
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• 제56권6호
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• pp.1000-1006
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• 2007

This paper presents a methodology to calculate an optimal solution of equilibrium to differential algebraic equations for power systems. It employs a nonlinear interior point method to solve the optimization formulation which includes dynamic equations representing the two-axis synchronous generator model with AVR and speed governing controls, algebraic equations, and steady-state nonlinear loads. This paper also adopts two algorithms for the improvement of solution convergence. In power system analysis and control, equilibrium optimization (EOPT) is applicable for diverse purposes that need the consideration of dynamic model characteristics at a steady-state condition.

• 제어로봇시스템학회논문지
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• 제14권12호
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• pp.1270-1277
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• 2008

A Haar wavelet based numerical method for solving singularly perturbed linear time invariant system is presented in this paper. The reduced pure slow and pure fast subsystems are obtained by decoupling the singularly perturbed system and differential matrix equations are converted into algebraic Sylvester matrix equations via Haar wavelet technique. The operational matrix of integration and its inverse matrix are utilized to reduce the computational time to the solution of algebraic matrix equations. Finally a numerical example is given to demonstrate the validity and applicability of the proposed method.