Exact Stiffness Matrices for Lateral–Torsional Buckling of Doubly Symmetric Tapered Beams with Axially Varying Material Properties

Soltani, Majid; Asgarian, Behrouz

doi:10.1007/s40996-020-00402-z

Cited by 11 publications

(11 citation statements)

References 72 publications

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“…where L expresses the element length, δε l ij is the linear parts of strain tensor in a variational form. By substituting equations (4a-c) into relation (9) yields…”

Section: Variational Formulationmentioning

confidence: 99%

“…The expression of the elastic strain energy variation can be formulated in terms of section forces acting on crosssectional contour of the elastic member in the buckled configuration. The resultants of classical stresses for beams with doubly symmetric I-section beam can be expressed as follows 3,9 N ¼…”

Section: Variational Formulationmentioning

confidence: 99%

“…Due to the importance of using tapered thin-walled beams having open and close cross-sections in different engineering fields such as steel frames, decks of the bridge, mechanical, and especially aeronautical components, the static and dynamic analyses of thin-walled structural elements with various end conditions under different loading cases have been widely studied in recent decades. [1][2][3][4][5][6][7][8][9][10] Lateral torsional-buckling is one of the instability modes in which the slender and laterally unbraced tapered thin-walled open section beam subjected to bending about its strong axis may suddenly buckle in a flexural-torsional mode. The web and flanges tapering parameters, the load height position, internal bending moment, and boundary conditions are the main factors affecting the lateral-torsional buckling strength of thin-walled beams with varying cross-section.…”

Section: Introductionsmentioning

confidence: 99%

“…The web and flanges tapering parameters, the load height position, internal bending moment, and boundary conditions are the main factors affecting the lateral-torsional buckling strength of thin-walled beams with varying cross-section. 1,2,9,10 With the development in high technology and fabrication processes, the practical applications of thin-walled laminate composite structural components have been extensively come into vogue in many advanced and innovative engineering systems such as axles of vehicles, space structures, helicopter rotors, wind turbine blades, and aircraft wings. The main reason for this increase is the conspicuous features 1 of fiber-reinforced composite materials, for instance, high fatigue resistance, durability, corrosion resistance, and high stiffness-to-weight and strength-to-weight ratios.…”

Section: Introductionsmentioning

confidence: 99%

See 3 more Smart Citations

Multi-objective optimization of lateral stability strength of transversely loaded laminated composite beams with varying I-section

Soltani

Abolghasemian

Shafieirad

et al. 2022

Journal of Composite Materials

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In this research, the lateral buckling analysis and layup optimization of the laminated composite of web and flanges tapered thin-walled I-beams based on maximizing lateral-torsional stability strength and minimizing mass/cost of the structure are investigated. The classical lamination theory and Vlasov’s model for thin-walled cross-section are adopted to establish the total potential energy for thin-walled symmetric balanced laminated beams with varying I-section. By implementing the Ritz method, an explicit formulation for the lateral-torsional buckling load of a double-tapered beam subjected to transverse loading is then derived in terms of the load height parameter and stiffness quantities. Subsequently, the optimal arrangements of layer sequences are obtained using the non-dominated sorting genetic algorithm (NSGA-II) and properly defined objective function. The critical factors of fitness function as lateral buckling strength and the mass of the structure with critical limitations as ply angle, number of layers for the web and flanges, and the thickness of all section walls are considered in this study. Finally, the optimal layer arrangement for the web and flanges are separately determined and discussed. The results show that the presented optimization procedure and layups patterns lead to increasing the lateral-torsional buckling capacity about 52% compared to the conventional angle-ply and unidirectional layups for the web and flanges, respectively.

show abstract

“…where L expresses the element length, δε l ij is the linear parts of strain tensor in a variational form. By substituting equations (4a-c) into relation (9) yields…”

Section: Variational Formulationmentioning

confidence: 99%

Section: Variational Formulationmentioning

confidence: 99%

Section: Introductionsmentioning

confidence: 99%

Section: Introductionsmentioning

confidence: 99%

See 2 more Smart Citations

Multi-objective optimization of lateral stability strength of transversely loaded laminated composite beams with varying I-section

Soltani

Abolghasemian

Shafieirad

et al. 2022

Journal of Composite Materials

View full text Add to dashboard Cite

show abstract

“…is process is repeated continuously to generate the weights of rbm1, so as to obtain the output data similar to the input data. e initial weight r 1 of a class of matrix equations is kept constant [13]. e hidden layer input data of the first RBM are substituted into the visual layer of the second RBM, and then the second RBM is trained.…”

Section: Construction Of Neural Network Structurementioning

confidence: 99%

Solving Bisymmetric Solution of a Class of Matrix Equations Based on Linear Saturated System Model Neural Network

Zhang

2021

Mathematical Problems in Engineering

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In order to solve the complicated process and low efficiency and low accuracy of solving a class of matrix equations, this paper introduces the linear saturated system model neural network architecture to solve the bisymmetric solution of a class of matrix equations. Firstly, a class of matrix equations is constructed to determine the key problems of solving the equations. Secondly, the linear saturated system model neural network structure is constructed to determine the characteristic parameters in the process of bisymmetric solution. Then, the matrix equations is solved by using backpropagation neural network topology. Finally, the class normalization is realized by using the objective function of bisymmetric solution, and the bisymmetric solution of a class of matrix equations is realized. In order to verify the solving effect of the method in this paper, three indexes (accuracy, correction accuracy, and solving time) are designed in the experiment. The experimental results show that the proposed method can effectively reduce the solving time, can improve the accuracy and correction effect of the bisymmetric solution, and has high practicability.

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Non-local finite element formulation for stability analysis of thin-walled nanobeams with varying I-section

Soltani

Atoufi

2022

Acta Mech

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Exact Stiffness Matrices for Lateral–Torsional Buckling of Doubly Symmetric Tapered Beams with Axially Varying Material Properties

Cited by 11 publications

References 72 publications

Multi-objective optimization of lateral stability strength of transversely loaded laminated composite beams with varying I-section

Multi-objective optimization of lateral stability strength of transversely loaded laminated composite beams with varying I-section

Solving Bisymmetric Solution of a Class of Matrix Equations Based on Linear Saturated System Model Neural Network

Non-local finite element formulation for stability analysis of thin-walled nanobeams with varying I-section

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