This study investigates the free vibration behaviors of functionally graded (FGM) plates with a porous structure, resting on a Kerr-type elastic foundation, while accounting for thermal effects and complex material property distributions. Within the framework of higher-order shear deformation theory (HSDT), two novel shape functions are introduced to accurately model transverse shear deformation across the plate thickness without employing shear correction factors. These functions are constructed to satisfy shear stress boundary conditions and capture nonlinear effects induced by material gradation and porosity. A variational formulation is developed to describe the dynamic response of FGM plates in a thermo-mechanical environment, incorporating temperature-dependent material properties and three porosity distributions: uniform, linear, and trigonometric. Numerical solutions are obtained using in-house MATLAB codes, allowing complete control over the formulation and interpretation of the results. The model is validated through detailed comparisons with existing literature, demonstrating high accuracy. The findings reveal that the porosity distribution pattern and gradient intensity significantly influence natural frequencies and mode shapes. The trigonometric porosity distribution exhibits favorable dynamic performance due to preserved stiffness in the surface regions. Additionally, the Kerr-type elastic foundation enables fine tuning of the dynamic response, depending on its specific parameters. The proposed approach provides a reliable and efficient tool for analyzing FGM structures under complex loading conditions and lays the groundwork for future extensions involving nonlinear, time-dependent, and multiphysics analyses.

A uniaxial material model for fatigue damage accumulation, established on the connection of unit elements, is presented in this paper. Although these units are regarded as micro-elements in the proposed model, they are based on a hysteretic operator that enables calculating hysteretic energy loss as an analytical expression. Further, this unit element represents a mechanical model with elastoplastic damage behavior in function of strain. The second level of modeling is defined by the connection of these units (micro-elements) with different values of total energy dissipated at failure. By changing the distribution of dissipated energy limit, various fatigue damage evolution laws are developed. Calculation of total and hysteretic energy loss in one loading cycle is also affected by fatigue damage as the varying number of unit elements are been eliminated when their maximum dissipation energy is reached. Material parameters for the model were defined based on the experimental monotonic and cyclic stress-strain tests, still, detailed comparison was not performed as the main advantage and aim of the paper was the development of the method for assessment of damage evolution in fatigue analysis. On the other hand, the number of cycles to failure ( N_f) and total heat dissipation are compared in both qualitative and quantitative aspects with experimental results. Finally, based on the proposed model, mean strain and load sequence effect diagrams were constructed. It is shown that the proposed model can provide a reliable estimation of fatigue life in the low-cycle regime of loading. The maximum error for the calculated N_f was 3% for constant strain loading for experiments with strain amplitude less than 5%. In load sequence fatigue life estimation, the proposed model demonstrated good accuracy, with a maximum error of 34%. Further, obtained results were achieved with different types of damage evolution that could be defined for the same material and fatigue life.

This article delivers a new Preisach model representing the correlation between the elastoplastic behavior of structural mild steel under axial monotonic and cyclic loading with damage. The newly formed model is based on the experimentally defined correlation between axial monotonic and cyclic behavior of structural mild steel. To examine the monotonic and cyclic behavior of structural mild steel and find fitting material properties for the model, monotonic and cyclic axial tensile tests are performed. Tests are executed on coupons of the commonly used European structural steel S275. The model represents a mathematical description of modified single-crystal material behavior under monotonic loading. Two different approaches were used to describe damage in the multilinear mechanical model. The excellent agreement with experimental results is achieved by infinitely linking many single-crystal elements in parallel, forming the polycrystalline model. This model provides a good solution for everyday engineering practice due to its geometric representation in the form of the Preisach triangle and the lower costs of monotonic tests used to define material properties compared to cyclic tests.

This study develops a quasi-3D higher-order shear deformation theory for the static analysis of laminated composite plates on elastic foundations. The seven-field kinematic formulation employs a single through-thickness function whose successive derivatives describe higher-order in-plane deformation, transverse shear, and transverse normal deformation. The central contribution is the variational derivation of a new seventh-order variational polynomial (SVP7) thickness function. Its coefficients are determined by minimizing a kinematic functional subject to symmetry, normalization, and zero transverse shear conditions at the free surfaces. The resulting function is the unique minimizer within the adopted seventh-order polynomial space and provides a monotonic decay of the shear-related thickness mode toward the free surfaces, without internal sign changes or spurious oscillations. The Winkler, Pasternak, and Kerr foundation models are incorporated within a unified energy formulation, and the governing equations for simply supported plates are solved using the Navier procedure. The formulation is validated against available three-dimensional elasticity solutions and existing higher-order theories in terms of nondimensional deflections and stress components over a range of plate thickness ratios. The results show consistent agreement with the reference solutions throughout the investigated thickness range and demonstrate the pronounced influence of foundation characteristics on the static response.

Timber-concrete composite (TCC) systems have application for new floors and for upgrading and enhancing of existing timber floors in residential and office buildings. In order to develop the optimal maintenance programs of structures, it is essential to predict the performance of structures over their life-cycle. The long-term behavior of timber-concrete composite floors is influenced by a combination of various factors, including material properties, load distribution, moisture effects, temperature effects and durability considerations. Timber and concrete material in the composite system, exhibit different behaviors over time due to their inherent characteristics. Deterioration prediction models are used to estimate the future degradation and condition of various types of structures. The aim of this paper is to present two probabilistic models, random variable deterioration rate model and stochastic gamma process model, that will capture uncertainty and variability associated with the deterioration of TCC floor under the service load and to estimate its service life.