受损加筋板极限强度及可靠性分析
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摘要
加筋板是船舶和海洋结构物中的基本结构构件。由于制作简单且有良好的强度重量比，加筋板也广泛应用于制造陆基结构物如箱梁和板梁桥等。由于船体梁的总体破坏通常由甲板、底板或者舷侧加筋板的屈曲或塑性破坏控制，因此在船舶结构设计中准确地计算甲板、底板或舷侧加筋板的极限强度就显得尤为重要。
随着高强度钢的广泛应用，板格屈曲大部分发生在弹性范围内，在后屈曲阶段当板格最大面内压缩应力处的等效应力达到屈服极限时，板格迅速卸载，此时板格达到极限强度。本文主要研究了各种缺陷和损伤对加筋板抗压极限强度的影响。由于准确的确定加筋板中带板的有效宽度十分重要，因此本文首先对加筋板中板格有效宽度进行了理论分析，在此基础上引入各种缺陷和损伤形式进行了大量的数值计算，定量研究了各种缺陷和损伤对板格抗压极限强度的折减。
本文考虑板中可能存在孔洞、腐蚀、裂缝、局部撞损和初始焊接变形或残余应力等损伤和初始缺陷，对不同的损伤形式用有限元程序(ANSYS)进行大量的计算，通过曲线拟合的方法引入折减系数对完好板格的有效宽度进行修正。在进行受损加筋板格极限强度计算时，按梁柱法采用修正的Perry-Robertson方程进行计算，其中有效带板的宽度取板格折减后的有效宽度。这样得到了一个含有各个参数的显式的极限强度公式。通过本文的研究工作，得出了以下几点结论：
1．联立弹性大变形法和刚塑性法求解板格极限强度，得到了一个简单的显式表达的完好板格极限强度公式，使得板格极限强度预报有了理论依据。
2．将板格的各种缺陷和损伤形式参数化，通过大量数值计算拟合出受损板格极限强度折减系数的以损伤参数为变量的显式表达示，用折减系数对完好板格极限强度进行折减得到受损板格极限强度公式。
3．在受损加筋板极限强度计算中，对有损伤的带板有效宽度取受损板格的有效宽度进行计算。
4．针对腐蚀这一损伤形式，应用现有统计资料对加筋板极限强度作了可靠性分析。
Stiffened steel panels are the basic strength members in ship and offshore structures. Due to their simplicity in fabrication and excellent strength to weight ratio, stiffened steel panels are also widely used for construction of land based structures such as box girder and plate girder bridges. Since the overall failure of a ship hull is normally governed by buckling and plastic collapse of the deck, bottom or sometimes the side shell stiffened panels, it is of crucial importance to accurately calculate the ultimate strength of stiffened panels in deck, bottom and side shell for more advanced structural design of ship structures.
The buckling of a plate mostly occurs in elastic regime with high strength steel adopted widely, and the plate reaches ultimate strength due to losing capacity when equivalent stress where maximal in-plane compressive stress appears arrives at yield in post-buckling phase. The elastic large deflection solution and rigid plastic solution are combined to achieve theoretical formula of ultimate compressive strength of a plate in the present paper, which agrees well with the result by the finite element calculation (ANSYS) and existing experiential expressions.
The reduction factors derived from curve fitting based on calculation results by the finite element program (ANSYS) considering all kinds of damages such as cutouts, corrosion, cracks, denting, initial deflection and residual stress are introduced to modify the effective width of perfect panel in the present paper. The modified Perry-Robertson equation is applied to calculate ultimate compressive strength of damaged stiffened panels founded on so-called beam-column method, and the width of effective plate adopts above reduced effective width of a damaged plate. Several conclusions are achieved in the present research as follow:
1. An explicit formula of ultimate strength is achieved according as combination of elastic large deflection method and rigid plastic method for perfect plates.
2. The explicit formulae with damage parameters as variable of reduction factors for ultimate strength of damaged plates are achieved by curve fitting based on a mass of numerical computation for parametric imperfection and damage of plates.
3. The effective width of damaged attached plates adopt the effective width of damaged plates in ultimate strength computation of damaged stiffened panels.
4. The reliability of ultimate strength of corroded stiffened panels is analyzed.
随着高强度钢的广泛应用，板格屈曲大部分发生在弹性范围内，在后屈曲阶段当板格最大面内压缩应力处的等效应力达到屈服极限时，板格迅速卸载，此时板格达到极限强度。本文主要研究了各种缺陷和损伤对加筋板抗压极限强度的影响。由于准确的确定加筋板中带板的有效宽度十分重要，因此本文首先对加筋板中板格有效宽度进行了理论分析，在此基础上引入各种缺陷和损伤形式进行了大量的数值计算，定量研究了各种缺陷和损伤对板格抗压极限强度的折减。
本文考虑板中可能存在孔洞、腐蚀、裂缝、局部撞损和初始焊接变形或残余应力等损伤和初始缺陷，对不同的损伤形式用有限元程序(ANSYS)进行大量的计算，通过曲线拟合的方法引入折减系数对完好板格的有效宽度进行修正。在进行受损加筋板格极限强度计算时，按梁柱法采用修正的Perry-Robertson方程进行计算，其中有效带板的宽度取板格折减后的有效宽度。这样得到了一个含有各个参数的显式的极限强度公式。通过本文的研究工作，得出了以下几点结论：
1．联立弹性大变形法和刚塑性法求解板格极限强度，得到了一个简单的显式表达的完好板格极限强度公式，使得板格极限强度预报有了理论依据。
2．将板格的各种缺陷和损伤形式参数化，通过大量数值计算拟合出受损板格极限强度折减系数的以损伤参数为变量的显式表达示，用折减系数对完好板格极限强度进行折减得到受损板格极限强度公式。
3．在受损加筋板极限强度计算中，对有损伤的带板有效宽度取受损板格的有效宽度进行计算。
4．针对腐蚀这一损伤形式，应用现有统计资料对加筋板极限强度作了可靠性分析。
Stiffened steel panels are the basic strength members in ship and offshore structures. Due to their simplicity in fabrication and excellent strength to weight ratio, stiffened steel panels are also widely used for construction of land based structures such as box girder and plate girder bridges. Since the overall failure of a ship hull is normally governed by buckling and plastic collapse of the deck, bottom or sometimes the side shell stiffened panels, it is of crucial importance to accurately calculate the ultimate strength of stiffened panels in deck, bottom and side shell for more advanced structural design of ship structures.
The buckling of a plate mostly occurs in elastic regime with high strength steel adopted widely, and the plate reaches ultimate strength due to losing capacity when equivalent stress where maximal in-plane compressive stress appears arrives at yield in post-buckling phase. The elastic large deflection solution and rigid plastic solution are combined to achieve theoretical formula of ultimate compressive strength of a plate in the present paper, which agrees well with the result by the finite element calculation (ANSYS) and existing experiential expressions.
The reduction factors derived from curve fitting based on calculation results by the finite element program (ANSYS) considering all kinds of damages such as cutouts, corrosion, cracks, denting, initial deflection and residual stress are introduced to modify the effective width of perfect panel in the present paper. The modified Perry-Robertson equation is applied to calculate ultimate compressive strength of damaged stiffened panels founded on so-called beam-column method, and the width of effective plate adopts above reduced effective width of a damaged plate. Several conclusions are achieved in the present research as follow:
1. An explicit formula of ultimate strength is achieved according as combination of elastic large deflection method and rigid plastic method for perfect plates.
2. The explicit formulae with damage parameters as variable of reduction factors for ultimate strength of damaged plates are achieved by curve fitting based on a mass of numerical computation for parametric imperfection and damage of plates.
3. The effective width of damaged attached plates adopt the effective width of damaged plates in ultimate strength computation of damaged stiffened panels.
4. The reliability of ultimate strength of corroded stiffened panels is analyzed.
引文
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[9] 胡勇，崔维成．无加筋平板极限强度的简化解析法与规范公式的比较．中国造船，2003，44(2)：8～15
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[20] 郑金鑫，崔维成．横向载荷作用下缺陷加筋板有效板宽的一个计算方法．航空学报，2002，23(1)：48～50
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[2] 吴连元．板壳理论．上海：上海交通大学出版社，1989．472～513
[3] 孙海虹，杨永谦，吴秀恒．采用奇异摄动法分析板格的极限强度．武汉交通科技大学报，1996，20(6)：733～738
[4] 陈铁云，沈慧申．结构的屈曲．上海：上海科学技术文献出版社，1993．97～110
[5] 胡毓仁，孙久龙．船体结构中受压矩形板计及残余应力影响的平均应力一平均应变曲线．上海交通大学学报，2001，34(1)：99～103
[6] 曾晓辉，戴仰山．单向压力作用下有初挠度矩形板的有效宽度和减缩有效宽度．中国造船，1998，3：57～65
[7] 曾晓辉，柳春图，冯玮．有初挠度简支矩形板的后屈曲特性．机械强度，2001，23(3)：263～267
[8] 陈念众，张圣坤，孙海虹．复合材料船体纵向极限承载能力分析．船舶工程，2001，5：51～53
[9] 胡勇，崔维成．无加筋平板极限强度的简化解析法与规范公式的比较．中国造船，2003，44(2)：8～15
[10] 王永军，崔维成，万正权．受双向压缩与垂向荷载联合作用下的船体平板极限承载能力计算．船舶力学，1998，2(2)：30～42
[11] 杜启端．开口薄板的稳定性分析．强度与环境，2000(4)：39～46
[12] 徐力，刘荣桂，韦芳芳．开孔板的有限元分析．江苏大学学报，2002，23(5)：28～30
[13] 方闯，曾广武．受压加筋板极限承载能力研究．华中理工大学学报，1998，26(11)：95～97
[14] 徐向东，崔维成．加筋板屈曲及极限强度分析．中国造船，1999，1：68～75
[15] 陈念众，张圣坤，孙海虹，复合材料船体纵向极限强度可靠性分析．中国造船，2002，43(2)：29～34
[16] 秦圣平，崔维成，沈凯．船舶结构时变可靠性分析的一种非线性腐蚀模型．船舶力学，2003，7(1)：94～102
[17] 徐向东，崔维成．船体梁与加筋板极限强度可靠性分析．船舶力学，2001，5(3)：48～57
[18] 白勇，徐向东，崔维成．船体结构极限强度的影响参数与敏感度探讨．船舶力学，1998，2(5)：35～43
[19] 何福志，万正权．船体结构总纵极限强度的简化逐步破坏分析．船舶力学，2001，5(5)：21～34
[20] 郑金鑫，崔维成．横向载荷作用下缺陷加筋板有效板宽的一个计算方法．航空学报，2002，23(1)：48～50
[21] 桑国光，张圣坤．结构可靠性原理及其应用．上海：上海交通大学出版社，1986
[22] 吴世伟．结构可靠度分析．北京：人民交通出版社，1986
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