전산구조공학 (Computational Structural Engineering)

한국전산구조공학회 (Computational Structural Engineering Institute of Korea)
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복합재료적층판의 진동해석을 위한 유한요소모델 I. 변분원리의 유도

Finite Element Analysis for Vibration of Laminated Plate Using a Consistent Discrete Theory Part I : Variational Principles

  • 발행 : 1994.12.01
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초록

적층판의 동적거동에 대한 유한요소해석모델개발을 목적으로 전단변형을 적합하게 고려한 적층판이론에 대한 변분원리를 유도하였다. 유도방법은 Sandhu 등에 의해 개발된 다변수 경계치문제의 변분원리이론을 따랐으며, 지배방정식의 미분연산자 매트릭스를 self-adjoint로 만들기 위하여 convolution을 이중선형사상으로 사용하였다. 유도된 적층판의 범함수에는 경계조건, 초기조건뿐만 아니라 유한요소해석모델에서 생길 수 있는 요소간 불연속조건도 포함시킬 수 있다. 상태변수의 적합함수공간을 확장하거나 특정조건을 적용하므로서 다양한 형태의 범함수를 유도할 수 있으며, 이를 통해 다양한 유한요소해석모델의 개발이 가능함을 논하였다.

A family of variational principles governing the dynamics of laminated plate has been derived using a variationally consistent shear deformable discrete laminated plate theory with particular reference to finite element procedures. The theoretical basis for the derivation is Sandhu's generalized procedure for the variational formulation of linear coupled boundary value problem. As the bilinear mapping to write the operator matrix of the field equations in self-adjoint form, convolution product was employed. Boundary conditions, initial conditions and probable internal discontinuity were explicitly included in the governing functionals. Some interesting extensions and specializations of the general variational principle were presented, which can provide many different finite element formulations for the problem.

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참고문헌

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