An exact analytical solution for a free-supported micropolar rectangle by the method of initial functions

Matrosov, Alexander V.

doi:10.1007/s00033-022-01714-y

Cited by 3 publications

(2 citation statements)

References 33 publications

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“…Te results of eigenfunctions of the boundary value problem are given as improper Fourier integrals or series expansions. Te MIF for micropolar media in plane strain conditions was also proposed by Matrosov [33]. In this study, he analysed a sample made of human bone, considering it a micropolar medium.…”

Section: Introductionmentioning

confidence: 74%

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Dynamic Analysis of Isotropic Homogeneous Beams Using the Method of Initial Functions and Comparison with Classical Beam Theories and FEM

Namdeo,

Dubey,

Dorji

2023

Complexity

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The main aim of this study is the dynamic analysis of isotropic homogeneous beams using the method of initial functions (MIFs) and comparison with classical beam theories and FEM. Also, this research employs the state space methodology, with a special emphasis on isotropy, to analyse simply supported beam systems. A mathematical model for the dynamic response of beams is constructed using the method of initial functions. The novelty of this study lies in its approach to dynamic analysis, where isotropic homogeneous beams are explored without making assumptions, thus ensuring increased precision using the method of initial functions. Importantly, the approach remains free from restrictive assumptions and relies solely on mathematical formulations, yielding results superior to classical beam theories such as Euler–Bernoulli, Timoshenko, and Rayleigh beam theories. In this work, the application of MIFs of various orders (4th, 6th, 8th, and 10th) to calculate natural frequencies is explored, enabling a thorough examination of the beam’s dynamic characteristics. In addition, parameters such as normal stresses, shear stresses, and deflections in different directions are considered to provide a comprehensive understanding of beam behaviour. To validate the findings, a detailed comparison with a finite element method (FEM) is conducted, achieving excellent agreement between the analytical results and FEM solutions. Furthermore, the influence of Poisson’s ratio (μ) on natural frequencies is investigated by varying its value from 0.18 to 0.30. The research also explores the deviation of plane stress values of the beam section from those estimated using the FEM for the corresponding components.

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Section: Introductionmentioning

confidence: 74%

“…Yet, its application is mostly seen in the feld of static analysis of the structure. It has been widely used in varied work of static analysis of structures by Matrosov [33]. Very few researchers and scientists have used the method in structural dynamics.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of Isotropic Homogeneous Beams Using the Method of Initial Functions and Comparison with Classical Beam Theories and FEM

Namdeo,

Dubey,

Dorji

2023

Complexity

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Symplectic solutions for orthotropic micropolar plane stress problem

Chen,

Tang,

et al. 2024

Acta Mech. Sin.

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Application of the Method of Initial Functions to Study Dynamics and Stress Distribution in Structural Members

Namdeo,

Dubey,

Biswas

et al. 2024

Advances in Civil Engineering

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This study investigates plate analyses employing the method of initial functions (MIFs) across various plate geometries and loading conditions. The conclusions derived from thick rectangular plates highlight substantial thickness‐induced effects on deflection and stress distributions. For thicker plates, the classical assumption of constant deflection fails, with maximum deflection often occurring at surfaces other than the middle plane. The classical and Reissner theories’ constant deflection assumption leads to significant discrepancies in thick plate deflection estimates, emphasizing the need for MIFs more accurate approach. Similarly, in the case of thick circular plates, deviations from classical theory are evident in radial and shear stress distributions, particularly pronounced closer to the plate edge and support. These deviations dissipate further away from these regions. Moreover, the study delves into free vibration analyses for rectangular and circular plates, revealing that classical theory tends to overestimate frequencies, especially as plate dimensions increase. Mindlin’s theory and MIF approaches showcase improved accuracy with increasing order, converging toward exact solutions. Additionally, Mindlin’s theory effectively captures the behavior of higher vertical modes, showcasing sign changes in characteristic quantities of the plate. The findings underscore the limitations of classical theories in accurately predicting plate behaviors, especially in thicker plates and higher modes of vibration. Conversely, the MIF method, alongside Mindlin’s theory, proves effective in providing nuanced insights into plate behaviors under various conditions, thus offering valuable implications for structural design and analysis.

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An exact analytical solution for a free-supported micropolar rectangle by the method of initial functions

Cited by 3 publications

References 33 publications

Dynamic Analysis of Isotropic Homogeneous Beams Using the Method of Initial Functions and Comparison with Classical Beam Theories and FEM

Dynamic Analysis of Isotropic Homogeneous Beams Using the Method of Initial Functions and Comparison with Classical Beam Theories and FEM

Symplectic solutions for orthotropic micropolar plane stress problem

Application of the Method of Initial Functions to Study Dynamics and Stress Distribution in Structural Members

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