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1
Content available A parametric study of higher-mode natural frequencies of composite stiffened cylindrical shell with cut-out
Chaudhuri Puja Basu, Sahoo Sarmila, Mitra Anirban
Engineering Transactions
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2023
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Vol. 71, iss. 1
81--109
EN
A finite element-based dynamic study of cut-out borne composite cylindrical shells reinforced with stiffeners is conducted. Isoparametric shell element with eight nodes and beam element with three nodes are used to study the mode-frequency behavior of shells with varied edge conditions. Anti-symmetric angle-ply laminates of two, four and ten layers with varying lamination angles are considered. Ten-layer laminates are investigated further as they exhibit better performance in fundamental frequency than two and four-layer laminates. The reduced integration method is adopted to find the shell element’s stiffness and mass matrices and the subspace iteration method is used for the eigenvalue solution of free vibration formulation. Natural frequencies for the first five modes are considered. The effects of fiber orientation angle (θ), degree of orthotropy (E11/E22), and width/thickness ratio (b/h) on the natural frequency are determined through numerical studies. It is revealed that vibration behavior strongly depends on both the number and arrangement of boundary constraints.
2
Content available Flexural Buckling Resistance of Stiffeners Reinforcing Wall of a Steel Silo
Marcinowski Jakub
Civil and Environmental Engineering Reports
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2023
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Vol. 33, no. 3
89--98
EN
Stiffeners reinforcing silo’s wall made from corrugated sheets are main structural elements sustaining meridional forces evoked by shear forces, source of which is friction of the material stored inside silo. Buckling resistance of stiffeners can be assessed by the method recommended in PN-EN 1993-4-1:2009/A1-2017-08E and in the draft of the Eurocode prEN 1993-4-1:2022. This method consists in determination of stiffener’s resistance treated as a column resting on elastic substrate which is the susceptible wall of the silo. It means that it was assumed that the stiffness of the sheeting resists buckling displacements normal to the silo wall. The procedure recommended in mentioned Eurocodes requires determination of stiffness coefficient K on the basis of the flexibility of an equivalent arch of the span equal to the double circumferential separation between adjacent stiffeners. The stiffness coefficient K was derived in the paper using classical mechanics methods and its value was compared to the one given in mentioned Eurocodes. Careful comparative analyses resulted in the identification of errors in one of the Eurocode formulae, which could result in a significant misestimation of the buckling resistance of the stiffeners. The proposed amendment led to a full correspondence between the final formula for K derived in the paper and that proposed in the referenced Eurocodes. The errors found were reported to the coordinator of the CEN working group updating EN 1993-4-1.
3
Content available remote Dent-to-stiffener evaluation concept for thin-walled steel cylinders
Akarsu Oğuzhan, Bayrak Bariş, Kiliç Mahmut, Maali Mahyar, Aydin Abdulkadir Cüneyt
Architecture Civil Engineering Environment
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2023
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Vol. 16, no. 3
43--54
EN
Defects/imperfections can occur during manufacturing, assembly, welding, and other processes, which can reduce the critical buckling load. However, the axial buckling load is beyond the scope of this work, and there are many studies on the stiffening effect of longitudinal dents. This concept combined the idea of the dent-to-stiffener evaluation concept for thin-walled steel cylinders. This study aims to transform the dents into artificial dents for a stiffening effect on the buckling phenomena. For this purpose, 37 thin-walled steel cylinder models, including the perfect model, were designed for varying dent shapes, dent widths, dent depths, dent lengths, and dent angles. The study also contributed to the effect of dent parameters on the critical buckling load of thin-walled steel cylinders. In particular, increasing the initial buckling will motivate the industry to convert dents into stiffeners with small artificial touches to enhance the longevity of the structure. The results showed that the introduction of certain artificial dents can significantly increase the critical buckling load of cylinders, thus improving their resistance against buckling, which has significant implications for various industries that use thin-walled steel cylinders in their structures. The proposed simulations for transforming dents into artificial stiffeners can be a valuable tool for enhancing the longevity and safety of thin-walled steel cylinders and other structures.
4
Content available Free vibration of composite cylindrical shells with orthogonal stiffeners
Wu Yongfu, Zhao Chen, Liang Haofeng, Yao Sishi, Xue Jianghong, Xu Peng
Journal of Theoretical and Applied Mechanics
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2022
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Vol. 60 nr 2
239--252
EN
This paper proposes theoretical and numerical approaches to scrutinize the free vibration of orthogonal stiffened cylindrical shells. According to K´arman-Donnell shell theory, the total energy of the stiffened cylindrical shells is derived. Based on the principle of minimum potential energy, the eigenfunction related to the frequency is established and solved by developing a Matlab program. Analytical solutions of the natural frequency for free vibraion of the stiffened cylindrical shells are calculated and are verified against the finite element results from ABAQUS software. On account of the observations from the parametric study, an optimization scheme of the stiffeners is proposed.
5
Content available Dynamical analysis of stiffened plates under patch loading
Srivastava A. K. L., Pandey S. R., Kumar A.
International Journal of Applied Mechanics and Engineering
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2013
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Vol. 18, no. 2
537--553
EN
The vibration characteristics of stiffened plates with cutouts subjected to in-plane partial edge loadings at one end at the plate boundaries are studied using the finite element method. Buckling loads and vibration frequencies are determined for different cutout ratios and extent of partial edge loading at one end. In the structural modelling, the plate and the stiffeners are treated as separate elements where the compatibility between these two types of elements is maintained. The main elegance of the formulation lies in the treatment of the stiffeners. The stiffeners can be placed anywhere within the plate element, and need not be placed on the nodal lines. The vibration characteristics are discussed and the results are compared with those available in the literature. Numerical results are presented for a range of cutout to plate size from 0 to 0.8.
6
Content available Vibration Analysis of Grid-Stiffened Circular Cylindrical Shells with Full Free Edges
Jam J. E., Yusef Zadeh M., Taghavian H. M, Eftari B.
Polish Maritime Research
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2011
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nr 4
23-27
EN
Free vibration of grid stiffened circular cylindrical shells is investigated based on the first Love’s approximation theory using Galerkin method. Full free edges are considered for boundary conditions. Anequivalent stiffness model (ESM) is used to develop the analytical solution of the grid stiffened circular cylindrical shell. The effect of helical stiffeners orientation and some of the geometric parameters of the structure have been shown. The accuracy of the analysis has been examined by comparing results with those available in the literature and finite element approach.
7
Content available Sensitivity analysis of buckling loads of bisymmetric I-section columns with bracing elements
Iwicki P.
Archives of Civil Engineering
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2010
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Vol. 56, nr 1
69-88
EN
The first order variation of critical loads of thin-walled columns with bisymmetric open cross-section due to some variations of the stiffness and location of bracing elements is derived. The considerations are based on the classical linear theory of thin-walled beams with non-deformable cross-section introduced by Vlasov. Both lateral braces and braces that restraint warping and torsion of the cross-section have been taken into account. In the numerical examples dealing with I-column, the functions describing the influence of location of the braces with unit stiffness on the critical load of torsional and flexural buckling are derived. The linear approximation of the exact relation of the critical load due to the variation of the stiffness and location of braces is determined.
PL
Wyznaczono pierwszą wariację siły krytycznej wyboczenia słupa o przekroju bisymetrycznym otwartym przy wariacji sztywności i położenia stężeń. Przyjęto założenia klasycznej teorii prętów cienkościennych o nieodkształcalnym przekroju poprzecznym. Analizowano zarówno stężenia boczne jak i stężenia ograniczające spaczenie oraz skręcenie przekroju poprzecznego. Stężenia modelowano jako podpory sprężyste. W przykładzie numerycznym zbadano wrażliwość siły wyboczenia skrętnego i giętego słupa o przekroju dwuteowym przy wariacji sztywności i położenia stężeń. Wyznaczono funkcje podcałkowe wrażliwości opisujące wpływ wprowadzenia wzdłuż długości pręta dodatkowych stężeń o jednostkowej sztywności na wartość siły krytycznej. Ponadto wyznaczono liniową aproksymację względnej wartości sił krytycznych pręta przy wariacji sztywności i położenia stężeń.
8
Content available remote Comparison of the theoretical load carrying capacity with the experimental data for some thin-walled plates and beams with intermediate stiffeners.
Teter Andrzej, Kołakowski Zbigniew
Archive of Mechanical Engineering
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2001
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Vol. 48, nr 1
29-54
EN
In the present paper, an analysis of lower bound estimation of the load carrying capacity of structures with intermediate stiffeners is undertaken. Thin-walled structures with intermediate stiffeners in the elastic range, being under axial compression and a bending moment, are examined on the basis of the Byskov and Hutchinson's method and the co-operation between all the walls of the considered structures is shown. The structures are assumed to be simply supported at the ends. The study is based on the numerical method of the transition matrix, using Godunov's orthogonalization. Instead of the finite strip method, the exact transition matrix method is used in this case. In the presented method for lower bound estimation of the load carrying capacity of structures, it is postulated that the reduced local critical load should be determined taking into account the global pre-critical bending within the first order non-linear approximation to the theory of the interactive buckling of the structure. The results are compared to those obtained from the design code and the data reported by other authors. The present paper is the continuation of papers, where the interactive buckling of thin-walled beam columns with central intermediate stiffeners in the first and the second order approximation was considered. The most important advantage of this method is that it enables us to describe a complete range of behaviour of thin-walled structures from all global (flexural, flexural-torsional, lateral, distortional and their combinations) to local stability. In the solution obtained, the effects of interaction of modes, the transformation of buckling modes with an increase in load, the shear lag phanomenon and also the effect of cross-sectional distortion are included.
PL
W prezentowanej pracy wyznaczono teoretyczne wartości nośności granicznej dla cienkościennych dźwigarów i płyt z centralnymi, wzdłużnymi żebrami pośrednimi obciążonych osiową siłą ściskającą i stałym momentem gnącym. Nieliniowe zagadnienie stateczności rozwiązano stosując teorię Byskova i Hutchinsona wykorzystując w obliczeniach numeryczną metodę macierzy przejścia. W prezentowanej metodzie oszacowania współczynników redukcji sztywności wzdłużnej postuluje się wyznaczenie zredukowanego lokalnego obciążenia krytycznego z uwzględnieniem globalnego do krytycznego zginania w ramach pierwszego nieliniowego rzędu przybliżenia teorii interakcyjnego wyboczenia konstrukcji. Otrzymane wyniki porównano z wynikami opublikowanymi przez innych autorów oraz z wartościami obliczonymi wg obowiązujących norm.
9
Finite element static analysis of stiffened shells
Samanta A., Mukhopadhyay M.
Applied Mechanics and Engineering
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1998
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Vol. 3, no 1
55-87
EN
Stiffened shell has been analyzed on the basis of a combination of Allman's plane stress triangle and DKT plate bending element. As the same displacement function is used for both the shell and the stiffener element, the compatibility condition at the shell beam junction is ensured. The formulation of the stiffener is done in such a manner that it can be placed anywhere within the shell element. The applicability of this element is tested for different structures, particularly for shallow and deep shells.
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