Mehmet Dorduncu

Stress wave propagation in adhesively bonded similar and dissimilar circular cylinders

This study addresses the wave propagation in adhesively bonded similar and dissimilar circular cylinders under an axial impulsive load. The four configurations are considered such as adhesively bonded aluminum–aluminum (Al–Al), steel–steel (St–St), aluminum–steel (Al–St), and steel–aluminum (St–Al) joints. The governing equations of the wave propagation are partial differential equations which are not usually amenable for analytical solutions under complex boundary conditions. Therefore, they are solved numerically using the finite difference method for spatial and temporal discretization. Each component of the adhesively bonded circular cylinders exhibits completely different stress and deformation states under an axial impulsive load. The axial displacement and axial stress components were dominant in both upper and lower adherends as well as the adhesive layer. The peak displacement levels became maximal in the bonded Al–Al and Al–St joints, decreased slightly in the bonded St–Al joint, and became minimal in bonded St–St joint. As the adhesively bonded joint becomes stiffer due to a stiffer (St) upper adherend, the bonded St–St and St–Al joints experience higher stress waves in comparison with those in the bonded Al–Al and Al–St joints, respectively. Moreover, the wave travels at a slightly higher speed through the adherend with a stiffer (St) material.

A refined zigzag element for modeling sandwich construction with embedded stiffeners

Stiffeners are commonly used to improve the load carrying capacity of a structure. Under general loading conditions, the stiff faces of the sandwich panel undergo significant transverse bending deformations while the stiffeners experience both in-plane and transverse bending deformations. Finite element analysis of such structures may require severe mesh refinement in order to achieve the desired accuracy; thus, leading to impractical computations. In this study, a new element is developed for the analysis of sandwich panels with internal and/or external stiffeners in order to achieve computational accuracy and efficiency.

Failure prediction in sandwich panels under blast loading using a refined zigzag element

This study describes the use of a refined zigzag finite element to investigate the dynamic response of sandwich panels subjected to blast loading. The time variation of blast loading is represented in the form of a triangle. The solution is achieved by using a novel adaptive time stepping algorithm. The accuracy of the present approach is established by comparison against 3-D finite element models.

Stress wave propagation in a functionally graded adhesive layer between two identical cylinders

ABSTRACT This study investigates the stress wave propagation in circular aluminum cylinders bonded with a functionally graded adhesive layer subjected to an axial impulsive load. The adhesive joint consists of two identical (aluminum) cylinders and a functionally graded adhesive layer. The volume fractions of the two constituents: aluminum and epoxy in the adhesive layer were functionally tailored through the adhesive thickness by obeying a power-law. Therefore, the effective material properties at any point in the adhesive layer were predicted by the Mori-Tanaka homogenization scheme. The governing equations of the wave propagation in the joint were discretized by means of the finite difference method. The influence of the compositional gradient exponent on the displacement and stress distributions of the joint was examined. It was observed that changing the material composition of the adhesive layer had an evident effect on the displacement and stress levels, especially in the lower cylinder. On the contrary, the influence of the compositional gradient exponent was found to be minor on the displacement and stress distributions. The displacement and stress distributions were also investigated along the upper and lower cylinder-adhesive interfaces. Accordingly, with increasing the ductility of the adhesive layer the waves transmitted to the lower cylinder caused lower displacement levels. The normal stresses become peak at the bottom corners of the upper and lower cylinder-adhesive interfaces whereas the shear stresses concentrate in the middle region of the interfaces. In addition, the temporal variations of the displacement and stress components were evaluated at some critical points of the adhesive and lower cylinder. The compositional gradient exponent played an important role on the displacement and stress levels as well as the wave speeds in the adhesive and lower cylinder rather than in the upper cylinder. The stresses in the joints were observed to be alleviated by employing a functionally graded adhesive layer.

Weak form of peridynamics

This chapter presents the weak form of the peridynamic (PD) governing field equations. They specifically concern the Poisson’s equation and Navier’s equation under in-plane loading conditions. Their weak forms derived based on the variational approach enable the direct imposition of nonlocal essential and natural boundary conditions. The numerical solution to these equations can be achieved by considering either a uniform or a nonuniform discretization.

Stress wave propagation in adhesively bonded functionally graded circular cylinders

This study investigates the stress wave propagation in adhesively bonded functionally graded (FG) circular cylinders subjected to an axial impulsive load. The volume fractions of the two constituent phases were assumed to vary according to a power law. The material properties of both upper and lower adherends, which are made of aluminum (Al) and silicon carbide (SiC) along the thickness direction, were calculated using the Mori–Tanaka homogenization scheme. The material composition was varied from the top ceramic to bottom metal layer (CM) for the upper adherend and metal to ceramic (MC) for the lower adherend. An epoxy-based adhesive was used to bond upper and lower adherends. The governing equations of the wave propagation in the adhesively bonded FG circular cylinder were discretized using the finite difference method. The distributions of the displacement and stress components at different times showed that the compositional gradient played a major important role on the displacement and stress levels as well as the wave speeds, whereas its influence on the displacement and stress profiles was minor. The axial displacement w(r, z) and axial stress components were found to be dominant displacement and stress components. The variations in the displacement and stress components vs. the time at the critical points of the adherend and adhesive layer indicated that the wave traveled at a slightly higher speed through the adherend with a stiffer (ceramic-rich) composition. Furthermore, the lower adherend underwent lower displacement and stress levels than those in the upper adherend since the adhesive layer behaved as a barrier to the stress wave propagation.

Ordinary-state based peridynamic truss element

This study presents a truss element that accounts for the peridynamic interactions among the finite element nodes. However, these interactions result in a sparsely populated global system stiffness matrix. Therefore, the skyline technique is used in the solution of resulting system of equations until damage initiates; then the explicit time integration to monitor damage progression. The major advantage of this element is the construction of the solution immediately before failure occurs with much less computational effort. In the absence of failure, the predictions from the peridynamic truss element are verified against finite element analysis with traditional elements. Also, a plate with a hole under tension is considered to demonstrate crack initiation and its propagation.