The buckling behavior of sandwich shells with functionally graded (FG) coatings operating under different external pressures was generally investigated under simply supported boundary conditions. Since it is very difficult to determine the approximation functions satisfying clamped boundary conditions and to solve the basic equations analytically within the framework of first order shear deformation theory (FOST), the number of publications on this subject is very limited. An analytical solution to the buckling problem of FG-coated cylindrical shells under clamped boundary conditions subjected to uniform hydrostatic pressure within the FOST framework is presented for the first time. By mathematical modeling of the FG coatings, the constitutive relations and basic equations of sandwich cylindrical shells within the FOST framework are obtained. Analytical solutions of the basic equations in the framework of the Donnell shell theory, obtained using the Galerkin method, is carried out using new approximation functions that satisfy clamped boundary conditions. Finally, the influences of FG models and volume fractions on the hydrostatic buckling pressure within the FOST and classical shell theory (CT) frameworks are investigated in detail.

This study investigates the influence of the soil–structure interaction (SSI) on the seismic performance of structures, focusing on the effects of foundation size, soil type, and superstructure height. While the importance of SSI is well recognized, its impact on structural behavior under seismic loads remains uncertain, particularly in terms of whether it reduces or amplifies structural demands. A simplified dynamic model, incorporating both the mechanical behavior of the soil and structural responses, is developed and validated to analyze these effects. Using a discrete element approach and the 1940 El Centro earthquake for validation, the study quantitatively compares the response of soil-interacting structures to those with fixed bases. The numerical results show that larger foundation blocks (20 m × 20 m and 30 m × 30 m) increase the seismic response values across all soil types, causing the structure to behave more like a fixed-base system. In contrast, reducing the foundation size to 10 m × 10 m increases the flexibility of structures, particularly buildings built on soft soils, which affects the displacement and acceleration response spectra. Softer soils also increase natural vibration periods and extend the plateau region in regard to spectral acceleration. This study further finds that foundation thickness has a minimal impact on spectral displacement, but structures on soft soils show more than a 15% reduction in spectral displacement (SD) compared to those on hard soils, indicating a dampening effect. Additionally, increasing the building height from 7 to 21 m results in a more than 20% decrease in SD for superstructures with natural vibration periods exceeding 2.4 s, while taller buildings with longer natural vibration periods exhibit opposite trends. Structures built on soft soils experience larger foundation-level displacements, absorbing more seismic energy and reducing earthquake accelerations, which mitigates structural damage. These results highlight the importance of considering SSI effects in seismic design scenarios to achieve more accurate performance predictions.

Truss systems are essential structural elements widely utilized for their lightweight design, high load-bearing capacity, and structural efficiency. This study introduces a novel energy-based method for analyzing time-dependent deformations in viscoelastic truss systems, applicable to both statically determinate and indeterminate configurations. The primary objective is to develop a total potential energy (TPE) functional that explicitly incorporates viscoelastic effects, system parameters, material properties, and loading conditions. Unlike conventional methods that treat viscous terms as non-conservative and lacking a clear energy representation, the proposed approach facilitates a direct and efficient energy-based formulation of the governing equations. The methodology employs the Laplace transform to simplify the problem and an inverse Laplace transform to recover solutions in the time domain. This systematic approach ensures accurate results while reducing computational effort, making it both time-efficient and straightforward to implement. A key advantage of the proposed method is its adaptability to various viscoelastic material models, such as the Kelvin–Voigt and Standard Linear Solid (SLS) models, and its applicability to diverse loading conditions, including step and impulsive loads. To validate the method, numerical analyses are conducted on truss systems subjected to different time-dependent loading scenarios. The results demonstrate the method’s capability to accurately predict the time-dependent behavior of viscoelastic trusses, addressing a significant gap in the literature by providing benchmark solutions. The proposed framework offers a computationally efficient alternative for analyzing viscoelastic structures, facilitating their integration into practical structural design and improving the prediction of long-term deformation behavior. This study provides a reliable and innovative solution for analyzing viscoelastic truss systems, making it a valuable tool for engineers and researchers working with time-dependent materials in structural applications.