• Computational Structural Engineering
• /
• v.4 no.2
• /
• pp.87-94
• /
• 1991

In this paper, a mixed variational principle applicable to the linear elasticity of inhomogeneous anisotropic materials is presented. For derivation of the general variational principle, a systematic procedure for the variational formulation of linear coupled boundary value problems developed by Sandhu et al. is employed. Consistency condition of the field operators with the boundary operators results in explicit inclusion of boundary conditions in the governing functional. Extensions of admissible state function spaces and specialization to a certain relation in the general governing functional lead to the desired mixed variational principle. In the physical sense, the present variational principle is analogous to the Reissner's recent formulation obtained by applying Lagrange multiplier technique followed by partial Legendre transform to the classical minimum potential energy principle. However, the present one is more advantageous for the application to the general anisotropic materials since Reissner's principle contains an implicit function which is not easily converted to an explicit form.

• Structural Engineering and Mechanics
• /
• v.73 no.1
• /
• pp.97-108
• /
• 2020

This study presents a 4 node, 11 DOF/node plate element based on higher order shear deformation theory for lamina composite plates. The theory accounts for parabolic distribution of the transverse shear strain through the thickness of the plate. Differential field equations of composite plates are obtained from energy methods using virtual work principle. Differential field equations of composite plates are obtained from energy methods using virtual work principle. These equations were transformed into the operator form and then transformed into functions with geometric and dynamic boundary conditions with the help of the Gâteaux differential method, after determining that they provide the potential condition. Boundary conditions were determined by performing variational operations. By using the mixed finite element method, plate element named HOPLT44 was developed. After coding in FORTRAN computer program, finite element matrices were transformed into system matrices and various analyzes were performed. The current results are verified with those results obtained in the previous work and the new results are presented in tables and graphs.

• Journal of Welding and Joining
• /
• v.18 no.4
• /
• pp.55-63
• /
• 2000

This paper presents a study of the solder bumping process. The theoretical model, based on the variational principle instead of solving the Navier-Stokes equation with moving boundaries, was developed to considered the energy dissipation in semi-solid phase and the approximate solidification time of the molten metal droplet. The simulation results revealed that the developed model could reasonably describe the collision behavior of molten metal with solid surface. Simulations were made with variation of initial droplet temperature, substrate metal and initial substrate temerature.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.29 no.5
• /
• pp.421-428
• /
• 2016

The present work extends the recent variational formulation to more general time-dependent problems. Thus, based upon recent works of variational formulation in dynamics and pure heat diffusion in the context of the extended framework of Hamilton's principle, formulation for fully coupled thermoelasticity is developed first, then, with thermoelasticity-poroelasticity analogy, poroelasticity formulation is provided. For each case, energy conservation and energy dissipation properties are discussed in Fourier transform domain.

• Geomechanics and Engineering
• /
• v.19 no.5
• /
• pp.463-472
• /
• 2019

The mode perturbation method (MPM) is suitable and efficient for solving the eigenvalue problem of a nonuniform soil deposit whose property varies with depth. However, results of the MPM do not always converge to the exact solution, when the variation of soil deposit property is discontinuous. This discontinuity is typical because soil is usually made up of sedimentary layers of different geologic materials. Based on the energy integral of the variational principle, a new mode perturbation method, the energy-based mode perturbation method (EMPM), is proposed to address the convergence of the perturbation solution on the natural frequencies and the corresponding mode shapes and is able to find solution whether the soil properties are continuous or not. First, the variational principle is used to transform the variable coefficient differential equation into an equivalent energy integral equation. Then, the natural mode shapes of the uniform shear beam with same height and boundary conditions are used as Ritz function. The EMPM transforms the energy integral equation into a set of nonlinear algebraic equations which significantly simplifies the eigenvalue solution of the soil layer with variable properties. Finally, the accuracy and convergence of this new method are illustrated with two case study examples. Numerical results show that the EMPM is more accurate and convergent than the MPM. As for the mode shapes of the uniform shear beam included in the EMPM, the additional 8 modes of vibration are sufficient in engineering applications.

• Journal of The Korean Astronomical Society
• /
• v.31 no.2
• /
• pp.89-93
• /
• 1998

An attempt is made to find the boundary tangential components of potential magnetic fields without constructing solutions in the entire domain. In our procedure, the magnetic energy is expressed as a functional of tangential and normal magnetic fields at the boundary and is minimized by the variational principle. This paper reports a preliminary study on two dimensional potential fields above a plane.

• Steel and Composite Structures
• /
• v.44 no.4
• /
• pp.473-488
• /
• 2022

A high-speed railway (HSR) bridge may undergo long-term deformation due to the degradation of material stiffness, or foundation settlement during its service cycle. In this study, an analytical model is set up to evaluate the influence of this long-term vertical bridge deformation on the track geometry. By analyzing the structural characteristics of the HSR track-bridge system, the energy variational principle is applied to build the energy functionals for major components of the track-bridge system. By further taking into account the interlayer's force balancing requirements, the mapping relationship between the deformation of the track and the one of the bridge is established. In order to consider the different behaviors of the interlayers in compression and tension, an iterative method is introduced to update the mapping relationship. As for the validation of the proposed mapping model, a finite element model is created to compare the numerical results with the analytical results, which show a good agreement. Thereafter, the effects of the interlayer's different properties of tension and compression on the mapping deformations are further evaluated and discussed.

• Korean Journal of Oriental Medicine
• /
• v.2 no.1
• /
• pp.337-380
• /
• 1996

'Nei Jing(內徑)' first defined the interrelationship of the true and tile false between evil factor affecting health(雅氣) and vital essence energy(精氣). According to 「'Nei Jing(內徑)', the above interrelationship is explained as 'If state of evil domination is considered as sthenia-syndrome(雅氣盛則實), if the consumption of healthy energy Is considered as asenia-syndrome(精氣尊則虛): 'Nei Jing(內徑)', proposed major features of the medicall treatment by 'regluate the vatal energy of asthenia and sthenia, treat the sthenia-syndrome by purgation, and treat the asenia-syndrome by therapy of invigoration(調其氣之虛實, 實則瀉之, 虛則補之): The above interrelationship was interpreted as 'treat the asthenia-syndrome of child organ by invigorating the mother organ(虛者補其母)'in the 69th of 'The Classic on Difficulty',(難經 六十九難). Go-Mu(高武) of Myung-dynasty describe therapy for invigoration and purgation of itself-meridian(自經 補瀉法), which locating acupuncture points according to the Therorr of Five Element in the five shu points of itself-meridian(自經 五유穴), based on the generation in the ${\ulcorner}$A Synthetical Book of Acupuncture and Moxibustion(針灸聚英)${\lrcorner}$, Sae-hyun Jang(張世賢) further extended location acupuncture points of the five shu points to the other-meridian in the ${\ulcorner}$Gyeo Jung Do Ju Nan Gyung(校正圖註難經)${\lrcorner}$ Sa-Ahm's 5 Element Acupuncture Method(舍嚴五行鍼法) was originated in 1644, the middle of the Yi-dynasty. It linked the reinforcing and reducing in acupuncture therapy which incorporated tlle asthenia-syndrome and sthenia-syndrome of the hollow organs, based on principle of the Yin Yang 5 Element Theory(陰陽五行學說), not only to the generation in the 5 element(相生關係) but also to the restriction in the 5 element(相剋關係). Furthermore it was devised for the medical treatment by comning therapy for invigoration and purgation of itself-meridian(自經 補瀉法) with that of the other-meridian. Even though many original forms(正形) of the therapy for invigoration and purgation of the Yin Yang 5 Element Theory comply with the principle of the generation and the restriction based on the principle of the Yin Yang 5 Element Theory are abailable, variational forms(變形) are also recognized by examining the nature of the Sa-Ahm's 5 Element Acupuncture Method(舍嚴五行鍼法), For this reason, it is very difficult to understand the Sa-Ahm's 5 Element Acupuncture Method(舍嚴五行鍼法) thoroughly. therefore, those variational forms are obstacles for the beginners to study the Sa-Ahm's 5 Element Acupuncture Method. In order to understand the principle of the practical clinical application of the Sa-Ahm's 5 Element Acupuncture Method, this study investigated which principle was based on the variations of the locating acupuncture points' method for the acupuncture prescription.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1994.10a
• /
• pp.121-128
• /
• 1994

A layerwise theory for the dynamic response of a laminated composite plate with integrated piezoelectric actuators and sensors subjected to both mechanical and electrical loadings is proposed. The formulation is derived form the variational principle with consideration for both total potential energy of the structures and the electrical potential energy of the piezoceramics. The governing equations of the present theory account for direct and converse effects of piezoelectrics, and layerwise variation of displacement field through the thickness of a laminate.

• Journal of Ocean Engineering and Technology
• /
• v.10 no.3
• /
• pp.96-104
• /
• 1996

Hamilton's principle is used to derive Euler-Lagrange equations for free surface flow problems of incompressible ideal fluid. The velocity field is chosen to satisfy the continuity equation a priori. This approach results in a hierarchial set of governing equations consist of two evolution equations with respect to two canonical variables and corresponding boundary value problems. The free surface elevation and the Lagrange's multiplier are the canonical variables in Hamilton's sense. This Lagrange's multiplier is a velocity potential defined on the free surface. Energy is conserved as a consequence of the Hamiltonian structure. These equations can be applied to waves in water of finite depth including generalization of Hamilton's equations given by Miles and Salmon.