• Coupled systems mechanics
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• v.13 no.2
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• pp.153-170
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• 2024

The problem considered in this theoretical paper is the delamination of a multilayered inhomogeneous beam structure that has viscoelastic behaviour under angle of twist, horizontal and vertical displacements which vary smoothly with time according to prescribed laws. The cross-section of the beam is a rectangle. The layers are made of different materials which are smoothly inhomogeneous along the length of the beam. The beam under consideration represents statically undetermined structure since it is clamped in its two ends. The problem of the strain energy release rate is solved. For this purpose, the strain energy stored in the beam structure is analyzed. In order to verify the solution obtained, the strain energy release rate is found also analyzing the time-dependent compliances of the beam under prescribed angle of twist and displacements. A parametric investigation is carried-out by applying the solution obtained. Special attention is paid to the effect of the parameters which control the variation of the angle of twist and the displacements with time on the strain energy release rate.

• Coupled systems mechanics
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• v.12 no.1
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• pp.69-81
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• 2023

This paper considers a delamination analysis of a statically undetermined inhomogeneous beam structure of rectangular section with viscoelastic behavior under torsion. The beam is built in at its two ends. The beam has two longitudinal inhomogeneous layers with a delamination crack between them. A notch is made in the upper crack arm. The external torsion moment applied on the beam is a function of time. Under these conditions, the beam has one degree of indeterminacy. In order to derive the strain energy release rate, first, the static indeterminacy is resolved. Then the strain energy release rate is obtained by analyzing the balance of the energy with considering the viscoelastic behavior. The strain energy release rate is found also by analyzing the compliance of the beam for checkup. Solution of the strain energy release rate in a beam without a notch in the upper crack arm is derived too. In this case, the beam has two degrees of static indeterminacy (the torsion moment in the upper crack arm is treated as an additional internal redundant unknown). A parametric investigation of the strain energy release rate is carried-out.

• Advances in materials Research
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• v.13 no.2
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• pp.87-102
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• 2024

This paper is focused on the delamination analysis of a multilayered beam structure loaded in torsion under strain-path control. The beam under consideration has a rectangular cross-section. The layers of the beam are made of different viscoelastic materials which exhibit continuous inhomogeneity in longitudinal direction. Since the delamination is located inside the beam structure, the torsion moments in the two crack arms are obtained by modeling the beam as an internally static undetermined structure. The strain energy stored in the beam is analyzed in order to derive the strain energy release rate (SERR). Since the delamination is located inside the beam, the delamination has two tips. Thus, solutions of the SERR are obtained for both tips. The solutions are verified by analyzing the beam compliance. Delamination analysis with bending-torsion coupling is also performed. The solutions derived are timedependent due to two factors. First, the beam has viscoelastic behavior and, second, the angle of twist of the beam-free end induced by the external torsion moment changes with time according to a law that is fixed in advance.

• Advances in nano research
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• v.12 no.6
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• pp.617-627
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• 2022

In the current study, the nonlinear impact of the Von-Kármán theory on the vibrational response of nonhomogeneous structures of functionally graded (FG) nano-scale tubes is investigated according to the nonlocal theory of strain gradient theory as well as high-order Reddy beam theory. The inhomogeneous distributions of temperature-dependent material consist of ceramic and metal phases in the radial direction of the tube structure, in which the thermal stresses are applied due to the temperature change in the thickness of the pipe structure. The general motion equations are derived based on the Hamilton principle, and eventually, the acquired equations are solved and modeled by the Meshless approach as well as a computer simulation via intelligent mathematical methodology. The attained results are helpful to dissect the stability of the MEMS and NEMS.

• Coupled systems mechanics
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• v.11 no.6
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• pp.543-556
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• 2022

Delamination of multilayered inhomogeneous beam that exhibits non-linear relaxation behavior is analyzed in the present paper. The layers are inhomogeneous in the thickness direction. The dealamination crack is located symmetrically with respect to the mid-span. The relaxation is treated by applying a non-linear stress-straintime constitutive relation. The material properties which are involved in the constitutive relation are distributed continuously along the thickness direction of the layer. The delamination is analyzed by applying the J-integral approach. A time-dependent solution to the J-integral that accounts for the non-linear relaxation behavior is derived. The delamination is studied also in terms of the time-dependent strain energy release rate. The balance of the energy is analyzed in order to obtain a non-linear time-dependent solution to the strain energy release rate. The fact that the strain energy release rate is identical with the J-integral value proves the correctness of the non-linear solutions derived in the present paper. The variation of the J-integral value with time due to the non-linear relaxation behavior is evaluated by applying the solution derived.

• Composites Research
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• v.33 no.6
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• pp.401-407
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• 2020

At the engineering and industrial areas, the lightweight composite material has been substituted with the metals, such as steel at the structural parts. This composite material has been applied by the adhesive bonding method, as well as the joint methods with rivets, welds or bolts and nuts. The study on the strength characteristics of adhesive interface is necessarily required in order to apply the method to composite materials. CFRP specimens as the fiber reinforced plastic composites were manufactured easily and this study was carried out. The static experiments were performed under the loading conditions of in-plane and out-plane shears with the inhomogeneous composite TDCB specimens with CFRP, aluminum (Al6061), and aluminum foam (Al-foam). Through the result of this study, the durability on the inhomogeneous composite structure with adhesive interface was investigated by examining the fracture characteristic and the point in time.

• Structural Engineering and Mechanics
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• v.60 no.5
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• pp.891-902
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• 2016

The beam structure with breathing cracks subjected to harmonic excitations was modeled by FEM based on Euler-Bernoulli theory, and a piecewise dynamical system was deduced. The precise integration method (PIM) was employed to propose an algorithm for analyzing the dynamic responses of the deduced system. This system was first divided into linear sub-systems, between which there are switching points resulted from the breathing cracks. The inhomogeneous terms due to the external excitations were tackled by introducing auxiliary variables to express the harmonic functions, hence the sub-systems are homogeneous. The PIM was then applied to solve the homogeneous sub-systems one by one. During the procedures, a predictor-corrector algorithm was presented to determine the switching points accurately. The presented method can provide solutions with an accuracy to a magnitude of $10^{-12}$ compared with exact solutions obtained by the theories of ordinary differential equations. The PIM results are much more accurate than Newmark ones with the same time step. Moreover, it is found that the PIM can maintain a high level of accuracy even when the time step increases within a relatively wide range.