A Koiter‐Newton approach for nonlinear structural analysis

Aerospace Science and Technology

Ruess

2016

Self Cite

Liang, K., and Nonlinear buckling analysis of the conical and cylindrical shells using the SGL strain based reduced order model and the PHC method. Aerospace Science and Technology, 55, There may be differences between this version and the published version. AbstractThin-walled conical and cylindrical shells subjected to axial compression often show a snap-back response in the presence of buckling. Newton iterations based path-following methods cannot trace reliably the snap-back response due to the extremely sharp turning angle near the limit point, and the original Koiter-Newton method also meets difficulties to achieve a complete post-buckling response beyond the limit point. In this paper, the improved KoiterNewton method is proposed to trace the post-buckling path of cylinders and cones, in the framework of the reducedorder modeling technique. The polynomial homotopy continuation (PHC) method is used to solve the lower-order nonlinear reduced order model reliably and efficiently. The simplified Green-Lagrange (SGL) kinematics which consider the stress redistribution after buckling are implemented into the construction of the reduced order model to produce accurate results for curved shells. The numerical results presented reveal that the improved method is a robust and efficient technology to achieve the entire nonlinear response for the snap-back case.

Section: The Improved Koiter-newton Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear buckling analysis of the conical and cylindrical shells using the SGL strain based reduced order model and the PHC method

Aerospace Science and Technology

Ruess

2016

Self Cite

“…It is convenient to consider perturbation loads that excite neighboring states of equilibrium to allow the system to change from the primary to a secondary equilibrium path. An appropriate selection of perturbation loads is discussed in detail in Liang et al Taking into account these loads, the third‐order form of the equilibrium equation may be extended to consider multiple loading of the form

scriptL false(normalΔ boldu false) + scriptQ false(normalΔ boldu, normalΔ boldu false) + scriptC false(normalΔ boldu, normalΔ boldu, normalΔ boldu false) + O false({(‖‖, normalΔ boldu)}^{4} false) = boldF ϕ,

…”

Section: Review Of the Koiter‐newton Approachmentioning

confidence: 99%

An efficient mixed variational reduced‐order model formulation for nonlinear analyses of elastic shells

Magisano

Numerical Meth Engineering

Garcea

et al. 2017

Summary The Koiter‐Newton method had recently demonstrated a superior performance for nonlinear analyses of structures, compared to traditional path‐following strategies. The method follows a predictor‐corrector scheme to trace the entire equilibrium path. During a predictor step, a reduced‐order model is constructed based on Koiter's asymptotic postbuckling theory that is followed by a Newton iteration in the corrector phase to regain the equilibrium of forces. In this manuscript, we introduce a robust mixed solid‐shell formulation to further enhance the efficiency of stability analyses in various aspects. We show that a Hellinger‐Reissner variational formulation facilitates the reduced‐order model construction omitting an expensive evaluation of the inherent fourth‐order derivatives of the strain energy. We demonstrate that extremely large step sizes with a reasonable out‐of‐balance residual can be obtained with substantial impact on the total number of steps needed to trace the complete equilibrium path. More importantly, the numerical effort of the corrector phase involving a Newton iteration of the full‐order model is drastically reduced thus revealing the true strength of the proposed formulation. We study a number of problems from engineering and compare the results to the conventional approach in order to highlight the gain in numerical efficiency for stability problems.

“…Here, the perfect cylinder means that there is no imperfection in the structure. At that time there was not sufficient computational power to carry out nonlinear structural analyses [10,11] which could accurately represent and predict the complex behavior of imperfection sensitive structures in the case of buckling, hence the accuracy of NASA knock-down factors relies heavily on the reliability of the experimental results. The manufacturing and experimental techniques [12] have been significantly improved since 1968.…”

Section: Introductionmentioning

confidence: 99%

A new robust design for imperfection sensitive stiffened cylinders used in aerospace engineering

Sci. China Technol. Sci.

Yongjie

Qin

et al. 2015

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A knock-down factor is commonly used to take into account the obvious decline of the buckling load in a cylindrical shell caused by the inevitable imperfections. In 1968, NASA guideline SP-8007 gave knock-down factors which rely on a lower-bound curve taken from experimental data. Recent research has indicated that the NASA knock-down factors are inclined to produce very conservative estimations for the buckling load of imperfect shells, due to the limitations of the computational power and the experimental skills available five decades ago. A novel knock-down factor is proposed composed of two parts for the metallic stiffened cylinders. A deterministic study is applied to achieve the first part of the knock-down factor considering the measured geometric imperfection, the other types of imperfections are considered in the second part using a stochastic analysis. A smeared model is used to achieve the implementation of the measured geometric imperfection for the stiffened cylinder. This new robust and less conservative design for the stiffened cylinders is validated by using test results.knock-down factor, NASA guideline SP-8007, stiffened cylinder, stochastic analysis, smeared model Citation:Liang K, Zhang Y J, Sun Q, et al. A new robust design for imperfection sensitive stiffened cylinders used in aerospace engineering.