New analytic buckling solutions of rectangular thin plates with all edges free

Li, Rui; Zheng, Xinran; Wang, Haiyang; Xiong, Sijun; Yan, Kun; Li, Peng

doi:10.1016/j.ijmecsci.2018.05.041

Cited by 61 publications

(18 citation statements)

References 30 publications

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“…A symplectic Hamiltonian formulation of thin plates was also introduced by Li et al in [19] to obtain analytic solutions for the free vibration problem. It has recently been extended to account for the buckling problem in [20] and thin cylindrical shell structures in [21]. While it constitutes a powerful method to obtain analytic solutions of boundary-value problems, it doesn't esasily extend to systems interconnected in a complex way.…”

Section: Related Workmentioning

confidence: 99%

A port-Hamiltonian approach to modeling the structural dynamics of complex systems

Warsewa

Böhm

Sawodny

et al. 2021

Applied Mathematical Modelling

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With this contribution, we give a complete and comprehensive framework for modeling the dynamics of complex mechanical structures as port-Hamiltonian systems. This is motivated by research on the potential of lightweight construction using active load-bearing elements integrated into the structure. Such adaptive structures are of high complexity and very heterogeneous in nature. Port-Hamiltonian systems theory provides a promising approach for their modeling and control. Subsystem dynamics can be formulated in a domain-independent way and interconnected by means of power flows. The modular approach is also suitable for robust decentralized control schemes. Starting from a distributed-parameter port-Hamiltonian formulation of beam dynamics, we show the application of an existing structure-preserving mixed finite element method to arrive at finite-dimensional approximations. In contrast to the modeling of single bodies with a single boundary, we consider complex structures composed of many simple elements interconnected at the boundary. This is analogous to the usual way of modeling civil engineering structures which has not been transferred to port-Hamiltonian systems before. A block diagram representation of the interconnected systems is used to generate coupling constraints which leads to differential algebraic equations of index one. After the elimination of algebraic constraints, systems in input-state-output (ISO) port-Hamiltonian form are obtained. Port-Hamiltonian system models for the considered class of systems can also be constructed from the mass and stiffness matrices obtained via conventional finite element methods. We show how this relates to the presented approach and discuss the differences, promoting a better understanding across engineering disciplines. A Matlab framework is available on http://github.com/awarsewa/ph_fem/ to facilitate the application of the methods to different problems.

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Section: Related Workmentioning

confidence: 99%

A port-Hamiltonian approach to modeling the structural dynamics of complex systems

Warsewa

Böhm

Sawodny

et al. 2021

Applied Mathematical Modelling

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“…For a panel with bonded joints loaded with a uniformly distributed load, the shear stress at the edge τ (x) according to [17] bonds is determined by relationship (12).…”

Section: A B S Ch S U Sh S U S H S U Ch S U S Ch S U Sh S U S H S U Cmentioning

confidence: 99%

“…The use of joints with increased resistance to longitudinal shear [9] allows their use as an alternative to adhesive joints [10,11]. It is also worth noting that conventional panels with sheathings made of wood-based materials, such as DSP [12], OSB [13], etc.…”

Section: Introductionmentioning

confidence: 99%

The wood composite ribbed panels on mechanical joints

Лабудин

Popov

Stolypin³

et al. 2019

E3S Web Conf.

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Structures in the form of ribbed panels with sheathings from sheet materials are used in construction of buildings and structures of various purposes: civil, industrial, agricultural, etc. Panels are universal enclosures and supporting structures, they can be used as coverings, floors, walls. Ribbed coating slabs simultaneously perform the functions of roof purline, floorboards, sheathing, provide heat and sound protection of the building. They are characterized by unification, high level of factory readiness; the ability to control the strength, sound and heat-insulating properties, and low density of materials used, which allows significantly reducing the cost of laying the foundation of the building. The paper presents the results of investigations of the influence of various parameters on the stress-strain state of panels (type of joints, coefficient of stiffness of the bonded joints, the magnitude of the span, the width of the panel, and the material of anisotropic sheathing).To solve this problem, the well-known solution of the plane stress problem is used (Faylon method), in which the constants of integration are determined as the Fourier series expansion coefficient of contour loads. As a result of numerical researches, reduction coefficients for bendable ribbed wood-composite panels with mechanical joints were obtained.

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“…They obtained exact solutions for both the stability equation and the buckling loads. Other recent studies on plate buckling include: Lopatin and Morozov [26], Jafari and Azhari [27], Zureick [28], Seifi et al [29], Li et al [30], Wang et al [31], Mandal and Mishra [32] and Bouazza et al [33].…”

Section: Introductionmentioning

confidence: 99%

Galerkin-Vlasov Variational Method for the Elastic Buckling Analysis of SSCF and SSSS Rectangular Plates

Onyia¹,

Rowland-Lato²,

Ike³

2020

International Journal of Engineering Research and Technology

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This paper presents the Galerkin-Vlasov variational method for the elastic buckling analysis of SSCF and SSSS rectangular plates. The thin plate problems studied are: (i) simply supported along two opposite sides x = 0, and x = a, clamped along the third side y = 0, and free along the fourth side y = b; (ii) simply supported along the four sides x = 0, x = a, y = 0 and y = b. In each case the edges x = 0 and x = a are subjected to uniform compressive load. Mathematically, the considered stability problem is a Boundary Value Problem (BVP) expressed by a domain fourth order partial differential equation (PDE) whose general solution should satisfy all the boundary conditions determined by the edge support conditions. By the Galerkin-Vlasov method, the unknown deflection shape function is chosen as the product of the eigenfunctions of a vibrating thin beam of identical span in the x direction and an unknown function of y(Gn(y)). The Galerkin-Vlasov variational integral equation is simplified using the Leibnitz rule, integration by parts and the orthogonality properties of the eigenfunctions of simply supported thin beams to a system of fourth order ordinary differential equations (ODEs). The general solution of the system of ODEs is obtained using trial function methods in terms of hyperbolic and trigonometric functions. The imposition of boundary conditions is used in each of the two cases to find the characteristic buckling equation. The buckling equation is obtained in each case as a transcendental equation, which is solved to obtain the eigenvalues from which the buckling loads are determined. The results obtained in each case for the buckling equation are identical to previous results obtained by other scholars who used classical methods and energy minimization methods. The results obtained for the buckling loads are in agreement with previously obtained solutions in the literature. The results obtained in each presented case in this study are found to be exact because exact shape functions were used in the x direction and the general solution was obtained for the domain PDE at every point in the plate domain. In addition, the solution obtained was made to satisfy all the boundary conditions at all the edges of the plate.

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New analytic buckling solutions of rectangular thin plates with all edges free

Cited by 61 publications

References 30 publications

A port-Hamiltonian approach to modeling the structural dynamics of complex systems

A port-Hamiltonian approach to modeling the structural dynamics of complex systems

The wood composite ribbed panels on mechanical joints

Galerkin-Vlasov Variational Method for the Elastic Buckling Analysis of SSCF and SSSS Rectangular Plates

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