#  서지주요정보
제한 조건하의 변분법에 의한 동탄성 접촉 문제의 해석 = A solution method for elasto-dynamic contact problems by constrained variational approach
서명 / 저자 제한 조건하의 변분법에 의한 동탄성 접촉 문제의 해석 = A solution method for elasto-dynamic contact problems by constrained variational approach / 허경재.
발행사항 [대전 : 한국과학기술원, 1991].
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등록번호

8001657

소장위치/청구기호

학술문화관(문화관) 보존서고

DME 9112

도서상태

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#### 초록정보

A solution method for dynamic analysis of elastic contact problems with rigid body motion under small deformation is presented. The contact surface is assumed unbonded and frictionless. The problem is first described by partial differential equations with inequalities denoting the geometric compatibility condition on the contact surface. A variational statement constrained by these side conditions is then proposed. The equivalence of the two descriptions is shown by considering the necessary conditions of the variational statement. An incremental from is obtained using the rigid body motion described by a moving coordinate system attached to the body. The geometric compatability conditions are accordingly linearized. The deforming body is discretized by the finite element method, while the nodal displacements are approximated by admissible basis functions over time increments. A possible discontinuity in the velocity due to contact is allowed in the representation. The Lagrange multiplier technique is employed to impose the geometric compatability condition of contact. For numerical implementation, several contact check points are selected conveniently at nodal points on the contact surface. In the time domain, the time point to check the contact condition is chosen at the final time of a time step. If the discontinuity in the velocity is negative, this discontinuity is considered occurred at the initial time in this time step. The resulting discretized system is formulated in the form of a linear complementarity problem, suitable for numerical calculation. Two examples are considered to show the implementations. The first one is about a longitudinal impact of two elastic rods for which an analytical solution is available. The obained contact force shows good agreement with the analytical solution. The second example is about the impact of an elastic sphere with a rigid plane. The results are discussed comparing with the quasi-static solutions by the Hertz model. It is observed that numerically obtained maximum contact forces are larger than that of the quasi-static solution and calculated duration of impact is shorter. Although the emphasis in the presentation has been on the analysis of two body contact, the method is directly applicable to multibody contact problems with arbitrarily selected check points. To apply the method to more practical problem, however, frictional conditions must be included with additional complexity.

#### 서지기타정보

청구기호 {DME 9112 [vii], 80 p. : 삽화 ; 26 cm 한국어 부록 : 선형 요소에서의 접촉 조건 저자명의 영문표기 : Gyoung-Jae Huh 지도교수의 한글표기 : 곽병만 지도교수의 영문표기 : Byung-Man Kwak 학위논문(박사) - 한국과학기술원 : 기계공학과, 참고문헌 : p. 51-55 Lagrange equations Surface, deformation of Finite element method 변분법 --과학기술용어시소러스 유한 요소법 --과학기술용어시소러스 접촉 문제 --과학기술용어시소러스 탄성 역학 --과학기술용어시소러스 Lagrange 방정식 --과학기술용어시소러스 Calculus of variations
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