B6
Buckling

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10:40
conference time (CEST, Berlin)
Developing FEA Standards for UK Submarine Design
26/10/2021 10:40 conference time (CEST, Berlin)
Room: B
R. Craven, D. Graham (QinetiQ, GBR); D. Tanner, K. Hughes (MOD, GBR)
R. Craven, D. Graham (QinetiQ, GBR); D. Tanner, K. Hughes (MOD, GBR)
Finite Element analysis has been slow to be applied to the general design of submarine pressure vessels, in part because of the reliability and efficiency of traditional semi-empirical methods, and partly, as an unstable buckling problem, it is quite difficult to solve. This paper will describe the development of a standardised approach to predicting the collapse behaviour of submarine pressure hulls. These can be deceptively simple structures, usually axisymmetric ring-stiffened cylinders, cones, hemispheres and occasionally other curved profiles, and the only significant design load is uniform hydrostatic pressure. However, the collapse process is difficult to model accurately as it involves geometric non-linearity, elasto-plastic material behaviour and loss of stability. The strength of a hull is sensitive to a range of fabrication effects such as; shape imperfections, dimensional variations and residual stresses due to cold bending of plating and welding. These effects have been assessed during the development of the standardised approach and the accuracy of the process has been quantified against experimental data and conventional analytical, and semi-empirical, solutions. A plugin that captures this process has been written for Abaqus, (although the process could be implemented in any general-purpose FE code). It allows quick generation of consistent, repeatable models, while providing the user with a degree of flexibility in the model details and analysis approach. A range of allowable shape imperfections in the form of critical buckling modes and other fabrication effects can be combined to create an idealised as-built or design shape. The algorithms in the plugin have also been adapted for use with process automation and optimisation software to carry out formal optimisation and ‘design of experiments’ studies, allowing the process to be used effectively in pressure hull design cycles. Capturing this process in a design standard will encourage the use of FE analysis in the design process, which will in turn allow designers to exploit the full capability of FE to expand their design horizons.
Buckling collapse, shape imperfections, residual stress, optimisation
11:00
conference time (CEST, Berlin)
Optimization of Structures Under Consideration of Buckling Conditions
26/10/2021 11:00 conference time (CEST, Berlin)
Room: B
N. Wagner (INTES GmbH, DEU)
N. Wagner (INTES GmbH, DEU)
A look into the literature of the last five years shows a growing interest in the consideration of buckling in the optimization of structures. Buckling is a stability problem. The load factors are determined by solving a generalized eigenvalue problem with the underlying structural stiffness matrix and the geometric stiffness matrix. Similar to structural dynamics, multiple eigenvalues may already exist or arise during optimization due to symmetries. The inherently associated numerical difficulties in calculating the sensitivities increase the complexity of the task compared to standard weight or compliance optimization. In addition, the buckling shapes may change during the optimization. Therefore, a mode tracking method is used to assess the correlation of the eigenmodes. In this paper, first an example of a shape optimization is presented and contrasted with a sampling analysis. Afterwards, a topology optimization using buckling constraints is conducted. Load factors can be used in the objective function or as constraints. Additional result variables that are not used as design constraints in the optimization can also be exported. All calculations are performed using literature examples in PERMAS. References: [1] Wook-han Choi, Jong-moon Kimn Gyung-Jin Park: Comparison study of some commercial structural optimization software systems, Structural and Multidisciplinary Optimization, Vol. 54, (2016), pp. 685--699. [2] Anders Clausen, Niels Age, Ole Sigmund: Exploiting additive manufacturing infi_x000C_ll in topology optimization for improved buckling load, Engineering, Vol. 2, (2016), pp. 250--257. [3] Robert Dienemann, Axel Schumacher, Sierk Fiebig: Considering linear buckling for 3D density based topology optimization, Proceedings of the 6th International Conference on Engineering Optimization (2019), pp. 394--406. [4] Quoc Hoan Doan, Dongkyu Lee, Jaehong Lee, Joowon Kong: Design of buckling constrained multiphase material structures using continuum topology optimization, Meccanica, Vol. 54, (2019), pp. 1179--1201. [5] Peter D. Dunning, Evgueni Ovtchinnikov, Jennifer Scott, H. Alicia Kim: Level-set topology optimization with many linear buckling constraints us- ing an e_x000E_cient and robust eigensolver, International Journal for Numer- ical Methods in Engineering, Vol. 107, (2016), pp. 1029--1053. [6] Xingjun Gao, Yingxiong Li, Haitao Ma, Gongfa, Chen; Improving the overall performance of continuum structures: A topology optimization model considering stiffness, strength and stability, Computer Methods in Applied Mechanics and Engineering, Vol. 359, (2020). [7] Peng Hao, Bo Wang, Kuo Tian, Gang Li, Yu Sun, Chunxiao Zhou: Fast procedure for non-uniform optimum design of stiffened shells under buckling constraint, Structural and Multidisciplinary Optimization, Vol. 55, (2017), pp. 1503--1516. [8] D. Manickarajah, Y. M. Xie, G. P. Steven: Optimisation of columns and frames against buckling, Computers and Structures, Vol. 75, (2000), pp. 45--54. [9] W. Szyskowski: Multimodal optimality criterion for maximum stability, International Journal Non-Linear Mechanics, Vol. 77, (1992), pp. 623--633. [10] Scott Townsend, H. Alicia Kim: A level set topology optimization method for the buckling of shell structures, Structural and Multidisciplinary Optimization, Vol. 60, (2019) pp. 1783-1800. [11] Nils Wagner, Reinhard Helfrich: Einfluss von Parametervariationen auf das Beulen von versteiften Laminatstrukturen, NAFEMS DACH Konferenz, Bamberg, 25-27 April 2016 [12] Dan Wang, Mostafa M. Abdalla, Weihong Zhang: Buckling optimiza- tion design of curved sti_x000B_eners for grid-stiffened composite structures, Composite Structures, Vol. 159, (2017), pp. 656--666.
Buckling, Shape Optimization, Topology Optimization
11:20
conference time (CEST, Berlin)
The Relevance of Analytical Formulations Predicting Stiffener Tripping
26/10/2021 11:20 conference time (CEST, Berlin)
Room: B
J. Reijmers, P. Nobel (Nevesbu, NLD)
J. Reijmers, P. Nobel (Nevesbu, NLD)
In search for the governing failure mode of externally pressurized submarine pressure hulls the focus is, due to its loading, drawn to elastic buckling, although the dimensioning of general pressure hull design and material limitations make them prone to collapse or plastic buckling. Collapse occurs due to the loss of plastic capacity after a non-linear growth of the fundamental deformation mode. Plastic buckling occurs if the fundamental deformation mode of the pressure hull is transitioned in a buckling mode, i.e. a mode with lower strain energy, and the plastic capacity is lost due to the extent of the deformation. A true bifurcation point is often hardly observed due to imperfections, which initiate the governing buckling mode. Question is why to spend so much effort to determine the elastic buckling pressures other than to ensure they are well above the collapse pressure and plastic buckling pressure? This paper focuses on the value of elastic buckling evaluation of the pressure hull frames, generally referred to as frame tripping. Some latest attempts in improving the accuracy of the analytical formulations will be questioned. Firstly, this study will compare non-linear buckling with linear-elastic material behaviour to elastic buckling by means of finite element analysis. Secondly, the non-linear elastic-plastic effects will be included too. Doing so, the effect of the geometrical non-linearity and material elastic-plastic non-linearity will be visible separately and will give an indication of the relevance of frame tripping results predicted by analytical elastic buckling formulations. Literature offers a variety on analytical formulations, each with an underlying idea to remove undesired assumptions that impair results. Even recently comprehensive formulations are published to establish an accurate value of the elastic tripping pressures. This paper will show whether those methods are still relevant in modern pressure hull design or not.
Submarine pressure hulls, Nonlinear FEA, Elastic buckling, Plastic buckling, Collapse
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