This study presents a unified computational framework for predicting and optimizing the vibrational response of porous plates on viscoelastic foundations through the integration of refined quasi-three-dimensional shear deformation theory and advanced optimization strategies. A trigonometric shear deformation function incorporating thickness stretching is employed to accurately capture the plate kinematics without requiring a shear correction factor. The plate–foundation interaction is represented using a three-parameter visco-Winkler–Pasternak foundation, and the governing equations are derived using Hamilton’s principle. The Navier solution is subsequently employed to determine the natural frequencies of the plate. The accuracy of the proposed formulation is established through comparison with benchmark results reported in the literature, demonstrating good agreement. A comprehensive parametric investigation is performed to examine the effects of porosity volume fraction ( φ ), power-law index (P), thickness ratio ( a/h ), and damping coefficient ( c_d ) on the non-dimensional frequency (NDF). The results indicate that an increase in porosity volume fraction consistently reduces the NDF due to the associated degradation in structural stiffness. To reduce the computational cost of repeated numerical simulations, a Random Forest-based surrogate model is developed using the generated dataset. The surrogate model demonstrates high predictive capability, achieving an R2 value of 0.987. The trained surrogate is subsequently integrated with Bayesian Optimization and Genetic Algorithm to efficiently explore the seven-parameter design space. The optimization yields a minimum NDF of 0.001463, outperforming the corresponding Genetic Algorithm result of 0.001671. The proposed framework therefore establishes a computationally efficient data-driven methodology for vibration prediction, parameter exploration, and optimal design of porous functionally graded plates resting on viscoelastic foundations.
It is well known that stretching–bending coupling in the governing equations of the functionally graded material (FGM) plates can be eliminated to simplify the bending analysis by using the physical neutral surface (PNS) approach. However, the existing PNS was derived based on the assumption that the Poisson’s ratio is constant along the plate thickness. In this paper, a novel generalized PNS approach for static bending of FGM plate based on the higher-order shear deformation plate theory is firstly developed by considering the Poisson’s ratio to be varied as the same law of the Young’s modulus in the thickness direction. Analytical expressions of the related six position parameters defining the new PNS are presented in terms of the stiffness coefficients which are determined by the through-thickness variation of the material properties. Consequently, the strain field and equivalent bending moments of the FGM plate are expressed solely in terms of the bending variables, namely transverse deflection and rotations, thereby eliminating the stretching–bending coupling induced by the deviation of the PNS from the geometrical middle plane (GMP). Furthermore, equivalent bending stiffnesses of the Levinson-type FGM plate are established for the cases with and without considering the Poisson’s ratio variation, and the influence of this variation on the equivalent bending stiffness is quantitatively evaluated for power-law ceramic–metal FGMs. Numerical results demonstrate that neglecting Poisson’s ratio variation can lead to significant discrepancies, with relative errors exceeding 5
The anti-plane shear problem of a finite-length crack moving at a uniform velocity along the interface of two different one-dimensional (1D) hexagonal piezoelectric quasicrystals (PQCs) is investigated. By using the Fourier transform, the mixed boundary-value problem is reduced to the solution of dual integral equations. Through theoretical derivation and numerical analysis, the mechanical characteristics and electrical responses of crack propagation are studied. Explicit solutions for the mechano-electro-elastic fields of the uniformly moving crack in the periodic plane and the dynamic field intensity factors at the crack tip are derived. Based on the maximum stress σ _zθ^j , the preferred direction of crack branching is predicted. Under this assumption, the preferred crack branch angle or kinking angle is analyzed. The influences of the crack moving velocity, applied loads, and material constants on the preferred crack propagation direction are numerically analyzed. The study reveals that interfacial properties between dissimilar PQCs play a significant role in determining preferred crack propagation paths and stress field distributions. Furthermore, when the crack propagation velocity exceeds the critical value, crack branching occurs, and the preferred branching angle increases with increasing velocity.
This study develops an analytical bending formulation for laminated composite plates resting on elastic foundations by coupling Murakami’s zigzag theory (MZT) with Winkler and Pasternak foundation models. The main motivation is that existing foundation-based plate formulations generally rely on classical or higher-order shear deformation theories, whereas zigzag-based models have rarely been extended to foundation-supported laminates. The governing equations are derived from the principle of virtual work and solved by Navier’s method for simply supported plates under bi-sinusoidal transverse loading. The proposed formulation is validated against benchmark solutions available in the literature for cross-ply and angle-ply laminates under different foundation stiffness parameters and stiffness ratios. The results show that the formulation reproduces the combined influence of interlaminar zigzag kinematics and substrate compliance: For the symmetric cross-ply laminate the central deflection differs from Pagano’s exact three-dimensional solution by − 1.94
Automated fiber placement technologies enable fabrication of variable-stiffness curved structures such as shallow arches, cylindrical panels, and shells. Among these, variable-stiffness shallow arches with freeform geometry exhibit intricate instabilities under transverse loading—branching, snapping, and looping—posing challenges for the complete tracing of equilibrium manifolds. Here, we adopt Timoshenko beam theory and isogeometric basis functions and incorporate a von Kármán-type geometric nonlinearity to analyze shallow arches. The nonlinear equilibrium equations, derived using the principle of minimum total potential energy, are numerically solved using a previously established technique that seamlessly integrates path-following, singularity-locating, and branch-switching algorithms. This work extends the framework to capture the complete equilibrium manifolds of variable-stiffness shallow arches, revealing how their nonlinear buckling mechanisms are governed by arbitrary geometries and laminate configurations. The accuracy of the proposed framework is verified by comparing present results for several benchmark problems with those reported in the literature. Numerical results are presented for shallow arches with elliptic, sinusoidal, parabolic, and freeform geometries under various support conditions and fiber angle layups.
