A Method of Stress Field-based Numerical Analysis for Adjusting Hull Girder Loads = 선체거더하중 조정을 위한 응력장 기반 수치해석방법

다국어 초록 (Multilingual Abstract)

The International Association of Classification Societies (IACS) has introduced the concept of Equivalent Design Wave (EDW) into its Common Structural Rules (CSR) for the design of bulk carriers and tankers. Currently, each classification society is expanding the application of the EDW concept to various commercial vessels such as LNG carriers and container ships, as well as ship-type offshore structures such as FPSOs. EDW stands for Equivalent Design Wave, which implements design loads calculated at a certain probability level. The wave loads are provided as rule-based formulas through probability statistical analysis, so designers do not need to perform complex probability statistical processing themselves. However, since it is difficult to satisfy the design value of the hull girder load by simply integrating the rule-based wave load, load adjustment is essential. The hull girder load consists of three force components acting in each axial direction, namely the axial force (AF), vertical shear force (VSF), and horizontal shear force (HSF), and three moment components acting in each axial direction, namely the torsional moment (TM), vertical bending moment (VBM), and horizontal bending moment (HBM).
There are two methods for adjusting the hull girder loads: the rule-based method proposed by the classification society and the quadratic programming (QP) method using optimization. The rule-based method matches only the four main components of the hull girder loads, and distributes the additional loads added by the adjustment as nodal forces using shear flow and simple beam theory. This process utilizes stress fields but introduces complexity in calculating shear flow. In contrast, the QP method adjusts the loads through an optimization problem that matches all six components and minimizes the magnitude of the loads. Since this method distributes the load directly to the nodes using the force field, a load concentration phenomenon may occur in the detailed model area. To understand the existing technology, we looked in detail at how to adjust the hull girder load using the reaction force in the midship model according to DNV regulations. Based on this, a three-step adjustment method considering all hull girder load components and a load distribution method utilizing stress fields were derived. In addition, a load adjustment technique that considers various model ranges and boundary conditions is developed to expand the application scope of the present method.
The three-step adjustment method divides the hull girder load into the VSF, HSF, TM groups and the AF, VBM, HBM groups to adjust them, and in the intermediate stage, the VBM and HBM are updated by the VSF and HSF. The first group is adjusted by the shear forces on the cross section, and the second group is adjusted by the axial forces. Load distribution using a stress field is a method of distributing the load by assuming the stress distribution of the hull cross-section as the stress distribution of a simple beam cross-section and considering the cross-sectional area of the elements. There is no need to calculate the complex shear flow of the rule-based method, and the load concentration phenomenon of the QP method can also be prevented. The load adjustment method considering boundary conditions is a method that offsets the reaction force occurring at the boundary or utilizes it for load adjustment.
The developed load adjustment technique was verified by applying it to a simple beam structure, a container ship, and an LNG carrier. In the beam structure, it was confirmed that an arbitrary load can be well matched by assuming the target load as a sine function. For container ships, validation was performed for various models and boundary conditions. The models used for verification were the whole ship, forebody, aftbody, and midship models, and free, aft-end fixed, fore-end fixed, and simply supported boundary conditions were used, respectively. In the case of the midship model, it was shown that the same structural analysis results can be obtained by applying not only the simple support boundary conditions but also the aft-end fixed and fore-end fixed boundary conditions, showing that it can be applied in various ways. For LNG carriers, load cases were generated and load adjustments were performed according to DNV rules for three types of cargo hold models (mid cargo hold, foremost cargo hold, and aftmost cargo hold). When liquid cargo such as LNG or ballast is considered as a pressure load, the axial component of the pressure load generates VBM at the bulkhead location of the tank. When calculating VBM from stresses in structural analysis, a sharp increase or decrease can be observed at the location of the tank's bulkheads. In load adjustment, we added an option to include or exclude the axial component of the pressure load depending on the circumstances of the calculated target VBM.
It has been verified and compared with the QP method for container ships and LNG carriers. The QP method exhibits load concentration and stress concentration phenomena near detailed model areas or elements with relatively thin thickness, but because it uses an optimization method, the average and deviation of the overall load size are small. It was confirmed that the phenomenon of load or stress concentration was prevented by replacing the load field used in the current QP method with a stress field. The developed method was compared with the QP method in a typical LNG carrier model, and it was confirmed that there was almost no difference in the structural analysis results according to load adjustment.

국문 초록 (Abstract)

국제선급협회 (IACS)는 벌크선과 유조선 설계를 위한 공통구조규칙 (CSR)에 등가설계파 (EDW) 개념을 도입하였다. 현재 각 선급 협회는 LNG 운반선, 컨테이너선 등 다양한 상선과 FPSO 등 선박형 해양 구조물에 EDW 개념의 적용을 확대하고 있다. EDW는 특정 확률 수준에서 계산된 설계 하중을 구현하는 등가설계파을 의미한다. 파랑 하중은 확률 통계 분석을 통해 rule 기반 공식으로 제공되므로 설계자는 복잡한 확률 통계 처리를 직접 수행할 필요가 없다. 그러나 rule 기반 파랑 하중을 단순히 적분하여 선체거더하중의 설계값을 만족시키는 것은 어렵기 때문에 하중 조정이 필수적이다. 선체거더하중은 각 축 방향으로 작용하는 세 가지 힘 성분, 즉 축력 (AF), 수평 전단력 (HSF), 수직 전단력 (VSF)과 각 축 방향으로 작용하는 세 가지 모멘트 성분, 즉 비틀림 모멘트 (TM), 수직 굽힘 모멘트 (VBM), 수평 굽힘 모멘트 (HBM)로 구성된다.
선체거더하중을 조정하는 방법에는 두 가지가 있다. 선급협회에서 제안한 rule 기반 방법과 최적화를 이용한 2차계획법(QP)이 있다. Rule 기반 방법은 선체거더하중의 네 가지 주요 성분만을 일치시키고, 조정으로 추가되는 하중을 전단류와 단순 보 이론을 이용하여 절점력으로 분배한다. 이 과정에서는 응력장을 활용하지만 전단류를 계산하는 데 복잡성이 있다. 반면, QP 방법은 6가지 모든 구성 요소를 일치시키고 하중의 크기를 최소화하는 최적화 문제를 통해 하중을 조정한다. 이 방법은 하중장을 이용하여 하중을 절점에 직접 분산시키므로 상세 모델 영역에서는 하중 집중 현상이 발생할 수 있다. 기존 기술을 이해하기 위해 DNV 규정에 따라 중앙부 모델에서 반력을 이용하여 선체거더하중을 조정하는 방법을 자세히 살펴보았다. 이를 바탕으로 모든 선체거더하중 성분을 고려한 3단계 조정 방법과 응력장을 활용한 하중 분포 방법을 도출하였다. 또한, 본 방법의 적용 범위를 확대하기 위해 다양한 모델 범위와 경계 조건을 고려하는 하중 조정 기법을 개발하였다.
3단계 조정 방법은 선체거더하중을 VSF, HSF, TM 그룹과 AF, VBM, HBM 그룹으로 나누어 조정하고, 중간 단계에서는 VSF와 HSF에 의해 VBM과 HBM이 업데이트 된다. 첫 번째 그룹은 횡단면의 전단 하중으로 조정되고, 두 번째 그룹은 축 하중에 의해 조정된다. 응력장을 이용한 하중분포는 선체 단면의 응력분포를 단순 보 단면의 응력분포로 가정하고, 요소의 단면적을 고려하여 하중을 분배하는 방법이다. Rule 기반 방법의 복잡한 전단류를 계산할 필요가 없고, QP방법의 하중 집중 현상도 방지할 수 있다. 경계조건을 고려한 하중 조정 방법은 경계에서 발생하는 반력을 상쇄하거나 이를 하중 조정에 활용하는 방법이다.
개발된 하중 조정 기법은 간단한 보 구조, 컨테이너선, LNG 운반선에 적용하여 검증되었다. 보 구조에서는 목표 하중을 사인 함수로 가정하여 임의의 하중을 잘 일치시킬 수 있음을 확인하였다. 컨테이너선의 경우 다양한 모델과 경계조건에 대한 검증이 수행되었다. 검증에 사용된 모델은 전선구조, 선수부, 선미부, 중앙부 모델이며, 각각 자유, 선미부고정, 선수부고정, 단순지지 경계조건이 사용되었다. 중앙부 모델의 경우 단순 지지경계조건뿐만 아니라 선미부고정, 선수부고정 경계조건을 적용하여도 동일한 구조해석 결과를 얻을 수 있어 다양한 적용이 가능함을 보였다. LNG 운반선의 경우, 세 가지 유형의 화물창 모델(중앙 화물창, 선수 화물창, 선미 화물창)에 대해 DNV rule에 따라 하중 케이스를 생성하고 하중 조정을 수행하였다. LNG나 밸러스트와 같은 액체화물을 압력하중으로 고려될 경우, 압력하중의 축성분은 탱크의 격벽 위치에서 VBM을 발생시킨다. 구조 해석의 응력으로부터 VBM을 계산할 때, 탱크의 격벽 위치에서 급격한 증가나 감소를 관찰할 수 있다. 하중 조정에서는 계산된 목표 VBM의 상황에 따라 압력 하중의 축 성분을 포함하거나 제외하는 옵션을 추가하였다.
컨테이너선과 LNG운반선에 대해 QP방법과 비교검증 되었다. QP방법은 상세모델 영역이나 두께가 비교적 얇은 요소 근처에서 하중집중 및 응력집중 현상이 나타나지만, 최적화 방법을 사용하기 때문에 전체 하중 크기의 평균과 편차가 작다. 현재 QP방법에서 사용하는 하중장을 응력장으로 대체함으로써 하중이나 응력집중 현상이 방지됨을 확인하였다. 개발된 방법으로 일반적인 LNG 운반선 모델에서 QP 방법과 비교한 결과, 하중 조정에 따른 구조 해석 결과에 거의 차이가 없음을 확인하였다.

목차 (Table of Contents)

• Abstract i
• Chapter 1 Introduction 1
• 1.1 Research background 1
• 1.2 Problem statement 10
• 1.3 Research objective 11
• Chapter 2 Current status of hull girder load adjustment: Rule-based method 13
• 2.1 Introduction 13
• 2.2 Existing procedures for hull girder load adjustment 16
• 2.2.1 Definition of FE model 17
• 2.2.2 Calculation of section properties 20
• 2.2.3 Generation of local load 21
• 2.2.4 Calculation of reaction force & local hull girder load 22
• 2.2.5 Calculation of target hull girder load 26
• 2.2.6 Longitudinal unbalanced force 28
• 2.2.7 Vertical shear force adjustment procedure 28
• 2.2.8 Vertical and horizontal bending moment adjustment procedure 34
• 2.2.9 Torsional moment adjustment procedure 37
• 2.2.10 Shear force distribution in a cross-section 38
• 2.2.11 Axial force distribution in a cross-section 39
• 2.3 Discussion of hull girder load adjustment and load distribution 40
• 2.3.1 Solution method for load adjustment equation 41
• 2.3.2 Consideration of different boundary conditions 41
• 2.3.3 Distribution of adjustment load and analysis results 42
• 2.4 Summary 43
• Chapter 3 Development of advanced hull girder load adjustment technique 46
• 3.1 Introduction 46
• 3.2 An advanced hull girder load adjustment technique 47
• 3.2.1 Definition of FE model 48
• 3.2.2 Calculation of section properties 51
• 3.2.3 Generation of local load 52
• 3.2.4 Calculation of reaction force & local hull girder load 53
• 3.2.5 Calculation of hull girder load difference 57
• 3.2.6 Calculation of reaction force for hull girder load difference 58
• 3.2.7 Adjustment of hull girder load 65
• 3.2.8 End-moment application for simply supported B.C. 72
• 3.2.9 Verification 72
• 3.3 Applied examples by box-girder 74
• 3.3.1 Definition of FE model 74
• 3.3.2 Calculation of section properties 75
• 3.3.3 Generation of local load 77
• 3.3.4 Calculation of reaction force & local hull girder load 77
• 3.3.5 Calculation of hull girder load difference 77
• 3.3.6 Calculation of reaction force for hull girder load difference 79
• 3.3.7 Adjustment of hull girder load 79
• 3.3.8 End-moment application for simply supported B.C. 84
• 3.3.9 Verification 84
• 3.4 Discussion of distribution of added load for load adjustment 88
• 3.4.1 VSF, HSF, TM adjustment comparison 89
• 3.4.2 VBM, HBM, AF adjustment comparison 90
• 3.5 Summary 92
• Chapter 4 Verification of the developed techniques for various boundary conditions: Case 1 = Container ship 94
• 4.1 Introduction 94
• 4.2 Procedure for hull girder load adjustment 95
• 4.2.1 Definition of hull girder load adjustment problem 95
• 4.2.2 Definition of FE model 96
• 4.3 Hull girder loads adjustment application 100
• 4.3.1 Verification of the adjustment results 100
• 4.3.2 Application to FE models with various boundary conditions 101
• 4.3.3 Whole ship model and local load effect 109
• 4.3.4 Midship model and boundary effect 110
• 4.3.5 Application to whole ship structural analysis 113
• 4.4 Discussion of load distribution in actual ship applications 117
• 4.4.1 Effect of element size and thickness 117
• 4.4.2 Variation of load adjustment equations 120
• 4.4.3 Comparison of results according to load adjustment equation 122
• 4.5 Summary 126
• Chapter 5 Verification of the developed techniques for axial load: Case 2 = LNG Carrier 129
• 5.1 Introduction 129
• 5.2 Procedure for hull girder load adjustment 131
• 5.2.1 Definition of hull girder load adjustment problem 131
• 5.2.2 Definition of FE model 133
• 5.3 Hull girder loads adjustment application 136
• 5.3.1 Verification of the adjustment results 136
• 5.3.2 Loading condition and cases 137
• 5.3.3 Midship cargo hold model 138
• 5.3.4 Aftmost cargo hold model 142
• 5.3.5 Foremost cargo hold model 145
• 5.3.6 Comparison with QP method 149
• 5.3.7 Comparison according to boundary conditions 153
• 5.4 Summary 158
• Chapter 6 Conclusion 160
• Reference 162
• Appendix A Local hull girder loads 169
• A.1 Structural weight 170
• A.2 Internal loads 170
• A.2.1 Static liquid Pressure 170
• A.2.2 Dynamic liquid pressure 171
• A.3 External loads 173
• A.3.1 Hydrostatic pressure 173
• A.3.2 Hydrodynamic pressure 173
• Appendix B Target hull girder loads 177
• B.1 Vertical bending moment 177
• B.1.1 Vertical still water bending moment 177
• B.1.2 Vertical wave bending moment 177
• B.1.3 Target hull girder vertical bending moment 178
• B.2 Vertical shear force 179
• B.2.1 Vertical still water shear force 179
• B.2.2 Vertical wave shear force 179
• B.3 Horizontal bending moment 180
• B.3.1 Horizontal wave bending moment 180
• B.3.2 Target hull girder horizontal bending moment 181
• B.4 Torsional moment 181
• B.4.1 Wave torsional moment 181
• B.4.2 Target hull girder torsional moment 182
• Appendix C Effect of axial component of the load in hull girder load calculation 183
• C.1 Axial load effect in cargo hold analysis 183
• C.2 Hull girder load adjustment in still water 186
• C.2.1 Lightweight distribution adjustment 186
• C.2.2 Trim adjustment 189
• C.2.3 Hull girder load calculation in still water 192
• C.3 Summary 194
• 초 록 195