This study investigates analytical solutions stresses and displacements of the functionally graded cylindrically curved beam subjected to the thermal load in the radial direction. The ends of this curved FGM beam is supposed to be guided in such a way that a displacement in circumferential direction may occur and that the radius of the middle surface remains unchanged. Then, couples act on those ends, giving rise to pure bending condition. It is assumed that the temperature distribution varies as a function of the radial coordinate and is in steady state. The modulus of elasticity varies with the power law through of the thickness of the curved FGM beam. Accordingly, by applying the general mixture law, the thermal expansion, the heat transfer coefficient and the volume fraction varies depending on the power law (except Poisson ratio). The curved FGM beam is assumed to be in plane stress state. Using the von Mises yield criterion, the effects of the values of power law index on the displacement and stresses of the curved beam is discussed. The inner surface of the curved FGM beam is steel and its outer surface is aluminum. At positive and negative temperatures, the effects of the yielding on the curved beam are investigated. It is observed that the starting of the plastic yielding is on the outer surface, inner surface and at the simultaneously on both surfaces. Communicated by Eleonora Tubaldi.

This study presents the free vibration analysis of a double tapered beam having linearly varying both thickness and width, by using finite element and component mode synthesis methods. To determine the natural frequency and mode shape of the double tapered cracked beam, the stiffness and mass matrices of the beam have been obtained. The crack in the beam is modeled as a massless spring, and the beam is divided into two subcomponents from the crack section. The stiffness of spring has been derived from the linear elastic fracture mechanics theory as the inverse of the compliance matrix calculated using stress intensity factors and strain energy release rate expressions. It has been observed that natural frequencies and mode shapes vary depending on the location of the crack, the depth of the crack and the aspect ratios of the beam. The results of the present study and those in the literature are compared and a great deal of consistency has been found.

Geometric discontinuities are unavoidable in additively manufactured polymer components and can significantly alter their mechanical response; however, their effects are rarely quantified in a systematic and geometry-comparative manner. In this study, the tensile behavior of FDM-printed PLA+ specimens with three different geometries—dog-bone, circular-hole, and U-notched (manufactured and tested in accordance with ASTM D638 (Type IV))—was experimentally and numerically investigated. Tensile tests were conducted using a universal testing machine equipped with an extensometer, while finite element simulations were performed using an experimentally calibrated Ramberg–Osgood-based elastic–plastic material model. The dog-bone specimens exhibited an ultimate tensile strength (UTS) of 41–43 MPa and a Young’s modulus of 3.06 GPa, representing the intrinsic material response under nearly homogeneous stress conditions. Circular-hole specimens maintained comparable strength (38–42 MPa) but showed reduced ductility (1.4–1.6%) and a slightly increased apparent modulus of 3.17 GPa due to localized deformation. In contrast, U-notched specimens displayed the highest apparent modulus (≈5.30 GPa) and nominal UTS (46–49 MPa), accompanied by a pronounced reduction in ductility (0.9–1.0%), indicating severe stress concentration and predominantly brittle fracture behavior. Finite element analysis showed excellent agreement with experimental results, with peak von Mises stresses reaching approximately 42 MPa for all geometries, corresponding closely to the experimentally measured tensile strength. These results demonstrate that geometric discontinuities strongly govern stress localization, apparent stiffness, and fracture initiation in FDM-printed PLA+ components. The validated Ramberg–Osgood-based modeling framework provides a reliable tool for predicting geometry-dependent mechanical behavior under quasi-static loading and supports geometry-aware design of additively manufactured polymer structures.

In this study, the effects of cracks in the columns of a single degree of freedom (SDOF) steel structure model on the system responses due to the decrease in the equivalent spring coefficient were investigated. The crack in the columns was modeled as an edge crack, and the crack was thought to behave like a spring. The crack is considered as the mode I crack type (opening mode) specified in linear fracture mechanics. In order to examine the responses of the system under the influence of different excitations, the changes in displacement, acceleration, and power spectral density responses under the influence of harmonic excitation at a frequency equal to the fundamental frequency of the SDOF model and six different earthquake excitations were examined.

The initiation of ductile fractures in medium-strength AW5754 and high-strength AW6082 aluminum alloys at different quasi-static strain rates and under multiaxial stress states was investigated through a series of tensile tests using various specimen geometries. The sensitivity of the stress triaxiality locus to variations in the loading rate was examined for these two aluminum alloy families. Fractographic and elemental analyses were also conducted via SEM and EDS. Numerical simulations based on the finite element method (FEM) were performed using ABAQUS/Standard to determine the actual stress triaxialities and the equivalent plastic strains at fracture. The numerical approach was validated by comparing the simulation results with the experimental findings. These simulations facilitated the generation of a stress triaxiality locus through a curve-fitting process. Among the considered fitting functions, an exponential function was selected as it provided the most accurate relation between the equivalent plastic strain at fracture and the corresponding stress state across different strain rates. The results reveal different strain rate dependencies for the two alloys within a very low strain rate range. The resulting stress triaxiality loci provide a valuable tool for predicting fracture strains and for more accurately evaluating stress states. Overall, the findings of this study significantly advance the understanding of the fracture initiation behavior of aluminum alloys under multiaxial loading conditions and their sensitivity to various quasi-static loading rates.