표제지
요 지
목차
NOMENCLATURE 9
제 1 장 서 론 17
1.1 연구 필요성 17
1.2 연구 배경 19
1.3 연구 목적 23
제 2 장 EFGM 의 수식화 26
2.1 이동최소자승법 26
2.2 C 항을 포함한 이동최소자승법 29
2.3 가중 함수 31
2.4 갤러킨 정식화 35
2.5 필수경계조건의 처리법 37
2.5.1 라그랑지 승수법 37
2.5.2 수정변분법 37
2.5.3 유한요소와 혼용하는 방법 38
2.5.4 변환법 38
2.5.5 특이가중함수를 사용하는 방법 39
2.5.6 벌칙함수법 39
2.6 적분법 40
2.6.1 적분칸을 이용하는 방법 40
2.6.2 절점적분법(nodal integration) 41
제 3 장 경계선점법 42
제 4 장 균열해석을 위한 이론 47
4.1 파괴의 모드 47
4.2 응력확대계수(stress intensity factor) 48
4.2.1 모드 Ι 의 균열 48
4.2.2 모드 ΙΙ 의 균열 49
4.3 균열의 진전방향 50
4.4 J 적분법 52
4.4.1 영역적분법 54
4.4.2 상호적분법(interaction integral) 56
4.5 균열진전 알고리즘 60
4.6 균열의 모델링 63
4.6.1 균열의 모델링방법 63
4.6.2 균열해석에서의 적분 65
4.6.3 Gauss-Seidel 법을 이용한 반복계산법 66
제 5 장 수치예제 및 결과 67
5.1 이차원문제 67
5.1.1 외팔보 문제 67
5.1.2 구멍을 갖는 무한평판문제 71
5.1.3 정적균열문제 72
5.2 오일러 보 및 얇은 평판 문제 75
5.2.1 오일러 보 문제 75
5.2.2 얇은 평판 76
5.3 영역적분을 이용한 균열해석 81
5.3.1 단일측면균열(single edge crack) 81
5.3.2 경사측면균열(slanted edge crack) 86
5.4 전단하중에 의한 균열진전문제 89
5.5 굽힘에 의한 균열진전문제 92
5.6 DCB 의 균열진전문제 95
제 6 장 결 론 101
참고문헌 103
Abstract 109
감사의 글 111
Fig. 1 Exponential and quartic spline weight functions 33
Fig. 2 Quartic spline weight function and its shape function 34
Fig. 3 Back cell types of meshless method for integration 41
Fig. 4 Three modes of loading that can be applied to a crack 47
Fig. 5 Local coordinate system at crack tip 48
Fig. 6 Path independent closed contour about the tip of a crack 52
Fig. 7 Crack growth modeling 60
Fig. 8 J domain integral region for crack growth analysis 62
Fig. 9 Variance of influence domain of node J to the crack growth 64
Fig. 10 Split of crack tip node and node arrangement for the next crack 64
Fig. 11 Added and deleted nodes at the crack tip for crack analysis 65
Fig. 12 Geometry and loading state of a cantilever beam 68
Fig. 13 Node arrangements for the analysis of the cantilever beam 68
Fig. 14 Solution convergence of the cantilever beam expressed by the energy error norm in accordance with a variety of the nodal distances in case of the regular node arrangement 69
Fig. 15 Node arrangement and the loading state of an infinite plate with a hole 71
Fig. 16 Comparison of the stress concentration factors obtained by various methods along the Y axis of the cantilever beam 72
Fig. 17 Plate with an edge crack under uniaxial stress 73
Fig. 18 Node arrangement and J-integral path for the crack problem 73
Fig. 19 Statically indeterminate beam under a partially distributed load 75
Fig. 20 Models for beam analysis 76
Fig. 21 Clamped square plate under a concentrated force at center 77
Fig. 22 Node arrangement for a quadrant of the clamped square plate 77
Fig. 23 Clamped circular plate under distributed load 79
Fig. 24 Node arrangement for a quadrant of the clamped circular plate 80
Fig. 25 Edge crack under tension load 84
Fig. 26 Edge crack under shear load 84
Fig. 27 Node arrangement for edge crack analysis 85
Fig. 28 Slanted edge crack under tension load 86
Fig. 29 Node arrangement for slanted edge crack analysis 88
Fig. 30 Crack growth in edge crack under shear load using 0.5 crack growth size 89
Fig. 31 Crack growth in edge crack under shear load using 0.3 crack growth size 90
Fig. 32 Crack path in edge crack under shear load for two crack growth sizes 90
Fig. 33 Geometry, dimensions and load of TPB(three point bend beams) specimen 92
Fig. 34 Node arrangement for TPB crack growth analysis 93
Fig. 35 Crack paths obtained from experimental and numerical tests 93
Fig. 36 Geometry of double cantilever beam(DCB) specimen 95
Fig. 37 Overall crack growth path in double cantilever beam specimen using crack growth sizea ai =8 96
Fig. 38 Overall crack growth path in double cantilever beam specimen using crack growth size ai =5 96
Fig. 39 Four steps of crack growth in double cantilever beam specimen using crack growth size ai =8 97
Fig. 40 Four steps of crack growth in double cantilever beam specimen using crack growth size ai =5 98
Fig. 41 Crack growth paths in double cantilever beam specimen for two crack growth sizes 99
Table 1 Tip deflections (at point A) normalized with respect to the exact solution of the cantilever beam 70
Table 2 Comparison of Meshless method results with respect to exact solution 74
Table 3 Comparison of the tip deflections (at point A) normalized with respect to the exact solution of the beam 76
Table 4 Variation of the normalized center deflections in clamped square plate according to an increase of the nodes 78
Table 5 Variation of the normalized center deflections in clamped square plate according to an increase of the Gauss point 78
Table 6 Variation of the normalized center deflections in clamped circular plate according to an increase of the nodes 80
Table 7 Stress intensity factors for edge crack under tension load calculated by various domain integral sizes 82
Table 8 Stress intensity factors for edge crack under shear load calculated by various domain integral sizes 83
Table 9 Stress intensity factors for slanted edge crack under tension load calculated by various domain integral sizes 88