Sen Yung Lee¹, Shin Yi Lu², Yen Tse Liu², Hui Chen Huang²

CMES-Computer Modeling in Engineering & Sciences, Vol.33, No.3, pp. 293-312, 2008, DOI:10.3970/cmes.2008.033.293

Abstract A new analytic solution method is developed to find the exact static deflection of a Timoshenko beam with nonlinear elastic boundary conditions for the first time. The associated mathematic system is shifted and decomposed into six linear differential equations and at most four algebra equations. After finding the roots of the algebra equations, the exact solution of the nonlinear beam system can be reconstructed. It is shown that the proposed method is valid for the problem with strong nonlinearity. Examples, limiting studies and numerical analysis are given to illustrate the analysis. The exact solutions are compared with the perturbation solutions.… More >

Sen Yung Lee¹, Sheei Muh Lin², Chien Shien Lee³, Shin Yi Lu³, Yen Tse Liu³

CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.1, pp. 27-36, 2008, DOI:10.3970/cmes.2008.030.027

Abstract An analytic solution method, namely the shifting function method, is developed to find the exact large static deflection of a beam with nonlinear elastic springs supports at ends for the first time. The associated mathematic system is a fourth order ordinary differential equation with nonlinear boundary conditions. It is shifted and decomposed into five linear differential equations and at most four algebra equations. After finding the roots of the algebra equations, the exact solution of the nonlinear beam system can be reconstructed. It is shown that the proposed method is valid for the problem with strong nonlinearity. Finally, examples and… More >

H.M. Lee¹, H.S. Park^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.29, No.1, pp. 29-44, 2008, DOI:10.3970/cmes.2008.029.029

Abstract This paper presents a computational model to estimate deformed shapes of beam structures using 3D coordinate information from terrestrial laser scanning (TLS). The model is composed of five components: 1) formulation of polynomial shape function, 2) application of boundary condition, 3) inducement of compatibility condition, 4) application of the least square method and 5) evaluation of error vector and determination of reasonable polynomial shape function. In the proposed model, the optimal degree of polynomial function is selected based on the complexity of beam structures, instead of using a specific degree of polynomial function. The chosen polynomial function for estimation is… More >

F. M. A. El-Saeidy¹

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.3, pp. 33-42, 2000, DOI:10.3970/cmes.2000.001.335

Abstract In rotating radial ball bearings supported on elastic casings with the bearing outer ring lightly fitted into the housing, the force due to the ball elastic contact is indeed a rotating load rolling over the housing. For accurate estimation of the dynamic deformations of the casing annulus (hole), which in turn affect the bearing tolerances and hence the magnitudes of the generated forces, effect of the load rotation (motion) should be considered. Considering the integral casing and the outer ring to be a plate, an isoparametric plane stress finite-element (FE) based analytical procedure is presented for the dynamic analysis of… More >

C.P. Hong¹, M.F. Zhu², S.Y. Lee¹

FDMP-Fluid Dynamics & Materials Processing, Vol.2, No.4, pp. 247-260, 2006, DOI:10.3970/fdmp.2006.002.247

Abstract In typical solidification processes the flow of molten metal is usually regarded as an unavoidable phenomenon potentially affecting the morphology of dendritic growth. Fundamental understanding of such flow is thus important for predicting and controlling solidification microstructures. This paper presents numerical simulations on the evolution of dendritic microstructures with melt convection. A two-dimensional modified cellular automaton (MCA) coupled with a transport model is developed to simulate solidification of binary and ternary alloys in the presence of fluid flow. This model takes into account the effects of the constitutional undercooling and curvature undercooling on the equilibrium interface temperature. It also considers… More >

G. Q. Xie¹, J. P. Wang², Q. L. Zhang¹

CMC-Computers, Materials & Continua, Vol.48, No.2, pp. 103-117, 2015, DOI:10.3970/cmc.2015.048.103

Abstract Small-scale effect on the static deflection of a clamped graphene sheet and influence of the helical angle of the clamped graphene sheet on its static deflection are investigated. Static equilibrium equations of the graphene sheet are formulated based on the concept of nonlocal elastic theory. Galerkin method is used to obtain the classical and the nonlocal static deflection from Static equilibrium equations , respectively. The numerical results show that the static deflection and small-scale effect of a clamped graphene sheet is affected by its small size and helical angle. Small-scale effect will decrease with increase of the length and width… More >

D. Pandit¹, N. Thomas², Bhakti Patel¹, S.M. Srinivasan¹

CMC-Computers, Materials & Continua, Vol.45, No.2, pp. 127-144, 2015, DOI:10.3970/cmc.2015.045.127

Abstract In this paper, a class of problems involving space constrained loading on thin beams with large deflections is considered. The loading is such that, the locus of the force application point moves along an arbitrarily predefined path, fixed in space. Both linear elastic as well as elastic-perfectly plastic materials are considered. A simplification is realized using the moment-curvature relationship directly. The governing equation obtained is highly non-linear owing to inclusion of both material and geometric non-linearity. A general algorithm is described to solve the governing equation using an incremental formulation coupled with Runge Kutta 4^th order initial value explicit solver.… More >

Hong-Hua Dai^1,2, Jeom Kee Paik³, S. N. Atluri²

CMC-Computers, Materials & Continua, Vol.23, No.2, pp. 155-186, 2011, DOI:10.3970/cmc.2011.023.155

Abstract The application of the Galerkin method, using global trial functions which satisfy the boundary conditions, to nonlinear partial differential equations such as those in the von Karman nonlinear plate theory, is well-known. Such an approach using trial function expansions involving multiple basis functions, leads to a highly coupled system of nonlinear algebraic equations (NAEs). The derivation of such a system of NAEs and their direct solutions have hitherto been considered to be formidable tasks. Thus, research in the last 40 years has been focused mainly on the use of local trial functions and the Galerkin method, applied to the piecewise… More >

Hong-Hua Dai^1,2, Jeom Kee Paik³, Satya N. Atluri²

CMC-Computers, Materials & Continua, Vol.23, No.1, pp. 69-100, 2011, DOI:10.3970/cmc.2011.023.069

Abstract In this paper, the global nonlinear Galerkin method is used to perform an accurate and efficient analysis of the large deflection behavior of a simply-supported rectangular plate under combined loads. Through applying the Galerkin method to the governing nonlinear partial differential equations (PDEs) of the plate, we derive a system of coupled third order nonlinear algebraic equations (NAEs). However, the resultant system of NAEs is thought to be hard to tackle because one has to find the one physical solution from among the possible multiple solutions. Therefore, a suitable initial guess is required to lead to the real solution for… More >

C. H. Cheng¹, S. C. Chen²

CMC-Computers, Materials & Continua, Vol.1, No.3, pp. 205-212, 2004, DOI:10.3970/cmc.2004.001.205

Abstract A shear mode piezoelectric actuator is applied to deflect the diaphragm of pressure chamber in the droplet ejector or inkjet printhead. The deflection of the bulge-diaphragm and resulting swept volume is analyzed by analytical and numerical method. With free-body treatment of the model, the analytical exact solutions for the two free bodies of bulge-diaphragm and piezoelectric beam were obtained. Also, the numerical solution by ANSYS is obtained to verify the analytical result. Besides, the whole-model solution coupling the bulge-diaphragm and piezoelectric beam together was obtained by ANSYS to compare with the result of free-body analysis. In order to estimate the… More >