• 제목/요약/키워드: energy variational principle

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이방성탄성문제의 혼합형변분원리 (A Mixed Variational Principle of Fully Anisotropic Linear Elasticity)

  • 홍순조
    • 전산구조공학
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    • 제4권2호
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    • pp.87-94
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    • 1991
  • 본고에서는 Sandhu등에 의해 개발된 다변수경계치문제의 변분모델화 방법을 이용하여 범함수의 독립변수로써 변위와 응력을 동시에 포함하는 이방성탄성문제의 혼합형변분원리(Mixed Variational Principle)를 유도한다. 탄성방정식을 내적공간에서 self-adjoint한 미분연산자매트릭스 방정식으로 표시한 후 다변수 경계치문제의 변분이론을 적용하므로써 일반적 범함수가 구해지며, 이때에 지배방정식의 미분연산자와 경계조건식의 연산자의 일관성 (Consistency)을 유지하므로써 경계조건도 체계적으로 범함수내에 포함시킬 수 있다. 이 일반적 범함수에서 미분연산자의 self-adjointness성질을 이용하여 응력함수의 도함수를 제거하고 탄성방정식중 특정식이 항상, 정확히 만족된다고 가정하므로써 원하는 혼합형변분원리의 범함수를 유도할 수 있다. 여기에서 유도된 변분원리는 최근 Reissner에 의해 개발된 변분원리와 유사한 물리적 의미를 가지나 유도방법이 다를 뿐 아니라 일반적 이방성탄성체에 적용할 때 보다 편리한 형태로 된다. 이 혼합형변분원리는 다양하게 응용될 수 있으나, 복합재료적층판과 같은 이질성, 이방성 평판이론, 또는 쉘이론의 유도에 유용하게 사용할 수 있다.

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Variational approximate for high order bending analysis of laminated composite plates

  • Madenci, Emrah;Ozutok, Atilla
    • Structural Engineering and Mechanics
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    • 제73권1호
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    • pp.97-108
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    • 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.

용융금속 액적의 고체표면 충돌거동 (Collision Behavior of Molten Metal Droplet with Solid Surface)

  • 양영수;손광재;강대현
    • Journal of Welding and Joining
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    • 제18권4호
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    • pp.55-63
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    • 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.

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확장 해밀턴 이론의 일반화에 대한 고찰 (Study on the Generalization of the Extended Framework of Hamilton's Principle in Transient Continua Problems)

  • 김진규;신진원
    • 한국전산구조공학회논문집
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    • 제29권5호
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    • pp.421-428
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    • 2016
  • 논문은 동역학의 새로운 변분이론인 확장 해밀턴 이론을 열 탄성과 공극 탄성에 적용하여 더욱 일반화하는 것에 그 주요 목적이 있다. 이를 위해 열 탄성학에 대한 이론 적용이 우선적으로 검토되었고, 열 탄성-공극 탄성의 유사성을 바탕으로 공극 탄성에까지 그 이론이 확장되었으며, 각 경우에 대한 푸리에 변환을 통해 그 적정성을 확인하였다.

Characteristic equation solution of nonuniform soil deposit: An energy-based mode perturbation method

  • Pan, Danguang;Lu, Wenyan;Chen, Qingjun;Lu, Pan
    • Geomechanics and Engineering
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    • 제19권5호
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    • pp.463-472
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    • 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.

OBTAINING BOUNDARY TANGENTIAL COMPONENTS OF POTENTIAL MAGNETIC FIELDS BY A VARIATIONAL METHOD

  • CHOE G. S.
    • 천문학회지
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    • 제31권2호
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    • pp.89-93
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    • 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.

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Analytical evaluation of the influence of vertical bridge deformation on HSR longitudinal continuous track geometry

  • Lai, Zhipeng;Jiang, Lizhong;Liu, Xiang;Zhang, Yuntai;Zhou, Tuo
    • Steel and Composite Structures
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    • 제44권4호
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    • pp.473-488
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    • 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.

사암침법(舍巖鍼法)의 변형(變形)에 관(關)한 연구(硏究) (The Study on The variational Forms of Sa-Ahm's 5 Element Acupuncture Method)

  • 김달호;김중한
    • 한국한의학연구원논문집
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    • 제2권1호
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    • pp.337-380
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    • 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.

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LAYERWISE FORMULATION OF PIEZOELECTRIC LAMINATED COMPOSITES

  • Lee, Jaehong-;Ham, Hee-Jung
    • 한국전산구조공학회:학술대회논문집
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    • 한국전산구조공학회 1994년도 가을 학술발표회 논문집
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    • pp.121-128
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    • 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.

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유한수심 자유표면파 문제에 적용된 해밀톤원리 (Hamilton제s Principle for the Free Surface Waves of Finite Depth)

  • 김도영
    • 한국해양공학회지
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    • 제10권3호
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    • pp.96-104
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    • 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.

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