New Fourier expansion for thermal buckling analysis of rectangular thin plates with various edge restraints

Tang, Xiaocheng; Guo, Chunqiang; Wang, Kaimin; Song, Dongrui; Zhang, Jinghui; Qi, Wenyue

doi:10.1007/s00419-023-02447-8

Cited by 3 publications

(4 citation statements)

References 46 publications

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“…sin(β n y)dxdy is an unknown constant. Imposing Stoke's transformation [57][58][59][60] over the trial function in Equation ( 7), one can obtain new Fourier expansions for the higher-order partial derivatives of plate deflections, which are shown below:…”

Section: Basic Equationsmentioning

confidence: 99%

“…This solution procedure could be extended to deal with problems of plates subjected to more complex edge conditions by combining Stoke's transformation technique. For example, through the application of Stoke's transformation in the double Sine series form solution, Tang [57,58] developed a modified two-dimensional Fourier series method for conducting new thermal buckling investigations for plates under classical/non-classical edge conditions. This method offers a significant advantage in overcoming boundary-continuous problems when employing Fourier series solutions for plate problems, making it promising for addressing plates subjected to diverse non-Levy-type boundary restraints.…”

Section: Introductionmentioning

confidence: 99%

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New Natural Frequency Studies of Orthotropic Plates by Adopting a Two-Dimensional Modified Fourier Series Method

Wu,

Li,

et al. 2024

Buildings

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The free vibration behavior of orthotropic thin plates, which are clamped at three edges and free at one edge, is a matter of great concern in the engineering field. Various numerical/approximate approaches have been proposed for the present problem; however, lack precise analytic benchmark solutions are lacking in the literature. In the present study, we propose a modified two-dimensional Fourier series method to effectively handle free vibration problems of plates under various edge conditions. In the given solution, the adopted trial function automatically satisfies several boundary conditions. After imposing Stoke’s transformation in the trial function and letting it satisfy the remaining boundary conditions, we can change the present plate problem into calculating several systems of linear algebra equations which are easily handled. The present method can be regarded as an easily implemented, rational, and rigorous approach, as it can exactly satisfy both the governing equation and the associated edge conditions. Another advantage of the present method over other analytical approaches is that it has general applicability to various boundary conditions through the utilization of different types of Fourier series, and it can be extended for the further dynamic/static analysis of plates under different shear deformation theories. Finally, all the novel analytical solutions are confirmed to be sufficiently accurate since they match well with the FEM results. The new analytic solution obtained may serve as a benchmark for validating other numerical and approximate methods.

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Section: Basic Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

New Natural Frequency Studies of Orthotropic Plates by Adopting a Two-Dimensional Modified Fourier Series Method

Wu,

Li,

et al. 2024

Buildings

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show abstract

“…Recently, a modified 2D Fourier series approach [52,53] was developed for accurate mechanical analysis of plates under classical/non-classical edge conditions through combining the Stoke's transformation and the Navier solution technique. The main advantage of this approach is that it can overcome the boundary-continuous problems that usually cannot be avoided by other semi-inverse methods.…”

Section: Introductionmentioning

confidence: 99%

New Accurate Flexural Analysis for Different Types of Plates in a Rectangular Sewage Tank by Utilizing a Unified Analytic Solution Procedure

Sun,

Zhang,

Huang

et al. 2024

Buildings

Self Cite

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In the present paper, a modified Fourier series approach is developed for new precise flexural analysis of three different types of concrete plates in a rectangular sewage tank. The bending problems of the bottom plate, side-plate, and the fluid-guiding plate are not easily solved via using the traditional analytic approaches. Based on the Fourier series theory, the present approach provides a unified semi-inverse solving procedure for the above plates by means of choosing three different kinds of Fourier series as the trial functions. Although all the trial functions are quite similar to the classical Navier-form solution, new, precise analytic flexural solutions for plates without Navier-type edge conditions (all edges simply-supported) are achieved, which is mainly attributed to employing the Stoke’s transform technique. For each case, the plate-bending problems are finally altered to deal with linear algebra equations. Furthermore, owing to the orthogonality and completeness of the Fourier series, the obtained solutions perfectly satisfy both the edge conditions and the governing partial differential equation of plates, which paves an easily implemented and rational way for engineers and researchers to provide new, exact designs of plate structures. The main contribution of this study lies in the provision of a unified solution procedure for addressing complex plate-bending problems across diverse boundary conditions. By employing a range of Fourier series types, this approach offers a comprehensive solution framework that accommodates the complexities inherent in plate analysis. The correctness of the present analytic solutions is verified against precise finite element method (FEM) results and ones available in the literature. Finally, the influences of foundation, edge conditions, and aspect ratio on flexural behaviors of plates are discussed in detail.

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“…During long-term high-temperature operation, the rigid bolt-connected platform experiences self-heating and expansion, resulting in platform warping, depression, and reduced positioning accuracy during mass transfer [17,18]. Therefore, eliminating the warping and depression caused by heating the nanopositioner and improving the positioning accuracy during the mass transfer is an urgent problem that needs to be solved.…”

Section: Introductionmentioning

confidence: 99%

A Novel Thermal Deformation Self-Stabilization Flexible Connection Mechanism

Feng,

Lin,

Tang

2024

Actuators

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In micro-LED chip repair, a nanopositioner is commonly used to adjust the positioning of the LED chip. However, during the bonding process, the heat generated can cause the positioning system to deform, leading to inaccurate alignment and poor-quality chip repair. To solve this issue, a novel flexible connection structure has been proposed that can eliminate thermal deformation. The principle of this novel flexible connection structure is that the thermal distortion self-elimination performance is achieved via three flexible connection modules (FCM) so that the thermal stress is automatically eliminated. First, the paper introduces the principle of thermal deformation elimination, and then the design and modeling process of the proposed structure are described. A heat transfer model is then developed to determine how temperature is distributed within the structure. A thermal deformation model is established, and the size of the FCM is optimized using a genetic algorithm (GA) to minimize the thermal deformation. Finite element analysis (FEA) is used to simulate and evaluate the thermal distortion self-elimination performance of the optimized mechanism. Finally, experiments are conducted to verify the reliability and accuracy of the simulation results. The simulations and experiments show that the proposed structure can eliminate more than 38% of the thermal deformation, indicating an excellent thermal deformation self-eliminating capability.

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New Fourier expansion for thermal buckling analysis of rectangular thin plates with various edge restraints

Cited by 3 publications

References 46 publications

New Natural Frequency Studies of Orthotropic Plates by Adopting a Two-Dimensional Modified Fourier Series Method

New Natural Frequency Studies of Orthotropic Plates by Adopting a Two-Dimensional Modified Fourier Series Method

New Accurate Flexural Analysis for Different Types of Plates in a Rectangular Sewage Tank by Utilizing a Unified Analytic Solution Procedure

A Novel Thermal Deformation Self-Stabilization Flexible Connection Mechanism

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