Automated Ritz Method for Large Deflection of Plates with Mixed Boundary Conditions

Al-Shugaa, Madyan A.; Al-Gahtani, Husain J.; Musa, Abubakr E. S.

doi:10.1007/s13369-020-04642-z

Cited by 9 publications

(3 citation statements)

References 28 publications

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“…Additionally, it can be applied to describe and solve various boundary value problems for shells, beams, and plates [155]. The Ritz method is among the well-known approaches that have been employed for solving many boundary value problems, which proves its capability and efficiency in predicting the bending behavior of composite laminated plates with boundary conditions including free edges [156][157][158][159][160][161][162][163]. Song et al [164] employed the Rayleigh-Ritz approach to determine the natural frequency of laminated composite cylindrical shells under arbitrary boundary conditions.…”

Section: Rayleigh-ritz and Galerkin Methodsmentioning

confidence: 99%

Analysis of Laminated Composite Plates: A Comprehensive Bibliometric Review

Odeh,

Al-Shugaa,

Al-Gahtani

et al. 2024

Buildings

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Laminated composite plates have become a crucial point of interest in the industry, with the need to ensure sustained and stable structures throughout the plates’ lifespan. This study conducted a bibliometric analysis using the Scopus database, gathering 8221 documents for further scrutiny based on the linked meta-data. Utilizing the VOS viewer software version 1.6.19, maps were generated from scientific publishing network data, illustrating connections between researchers’ nations and keywords. The investigation into co-occurring phrases associated with laminated composite plates employed author keywords. The results reveal a significant and close relationship among top authors, suggesting a strong research connection, with the United States and China leading the field. Top cited documents and keyword correlations are examined to gauge current research interests. These critical reviews serve as essential resources for scholars and practitioners in the field. Additionally, the review discusses the advancements in and practical applications of different theories for laminated composite plates, with a focus on a bibliometric study using the Scopus database. This paper categorizes models within the context of an equivalent single-layer laminate, analyzing variations in established theories and methodologies for modeling laminated composite plates to offer a nuanced understanding of approaches and assessments in this field.

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Section: Rayleigh-ritz and Galerkin Methodsmentioning

confidence: 99%

Analysis of Laminated Composite Plates: A Comprehensive Bibliometric Review

Odeh,

Al-Shugaa,

Al-Gahtani

et al. 2024

Buildings

Self Cite

View full text Add to dashboard Cite

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“…11 The first step of the method is to find a suitable approximative function, which satisfies the geometric boundary conditions. 12,13 Initial geometric imperfections of the rectangular plate associated with zero initial stress are denoted by normal displacement w 0 ; in-plane initial imperfections are neglected. Therefore, the approximative function is expressed by:…”

Section: Mechanical Modellingmentioning

confidence: 99%

Improving climate resilience: Reduced-order mechanical modelling of a temperature-adaptable sun protection facade system

Schneider

Hückler

et al. 2023

Composites and Advanced Materials

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Analytical models to describe the mechanical behaviour of an adaptive sun protection facade system (Adaptex) are presented. First, a one-dimensional (1D) rigid link model is developed. Stretching and bending deformation of textile bands are represented with the aid of extensional and rotational springs respectively. The model is described by two generalized coordinates only. The second analytical model employs a continuous description based on the Kirchhoff plate theory. The Rayleigh–Ritz method is applied to analyse the deformation behaviour of the textile bands. In comparison with the experimental results, it can be found that the continuous model simulates the real deformation of the facade system, thus its morphological behaviour, very effectively. The results of a parametric study indicate that the stiffness of the textile bands, the geometric dimensions and the position of load application have significant effects on the deformation behaviour.

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“…It is di cult to obtain exact solutions to these large de ection problems, so people mainly study their numerical solutions and approximate analytical solutions by various methods and theories. Vincent [1] applied the perturbation method to solve the bending problem of a circular thin plate under a uniformly distributed load; Qian [2] used the central de ection as the perturbation parameter to solve the large de ection problems by the perturbation method; Nguyen-Van et al [3] studied the large de ection problems of plates and cylindrical shells with an e cient four-node at element with mesh distortions; Madyan et al [4] proposed an automated Ritz method for the large defection problem of plates with mixed boundary conditions; Yu et al [5] studied the nonlinear analysis for the extreme large bending de ection of a rectangular plate on nonuniform elastic foundations; Wang et al [6] proposed a wavelet method for the bending of circular plate with large de ection; Sladek et al [7] gave an iterative solution of large de ection problem of thin plates by the local boundary integral equation method; Yun et al [8] used the homotopy perturbation method to solve the large de ection problem of a circular plate; Yun et al [9] obtained new approximate analytical solution of the large de ection problem of a uniformly loaded thin circular plate with edge simply hinged by the Adomian decomposition method; Gbeminiyi et al [10] considered free vibration analysis of thin isotropic rectangular plates submerged in uid by the Adomian decomposition method and so on.…”

Section: Introductionmentioning

confidence: 99%

New Analytical Solution of the Large Deflection Problem of a Circular Thin Plate with Edge Clamped but Sliding Freely Under a Combined Loading

Zhao

Yun

2022

Mathematical Problems in Engineering

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This paper intends to study the large deflection problem of a circular thin plate with an edge clamped but sliding freely under the combined action of uniformly distributed load and centrally concentrated load by the Adomian decomposition method. If the uniformly distributed load is not decomposed, the parameters obtained by the Adomian decomposition method are the same as the perturbation solution studied by scholars before. If the uniformly distributed load is decomposed into a finite series, a new analysis solution can be obtained through the Adomian decomposition method. From the error comparisons between the new solution in this paper and the perturbation solution, one can see that the result in this paper is better. Finally, the internal stress and deflection are discussed through the graphics based on the new analysis method.

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Automated Ritz Method for Large Deflection of Plates with Mixed Boundary Conditions

Cited by 9 publications

References 28 publications

Analysis of Laminated Composite Plates: A Comprehensive Bibliometric Review

Analysis of Laminated Composite Plates: A Comprehensive Bibliometric Review

Improving climate resilience: Reduced-order mechanical modelling of a temperature-adaptable sun protection facade system

New Analytical Solution of the Large Deflection Problem of a Circular Thin Plate with Edge Clamped but Sliding Freely Under a Combined Loading

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