PSI - Issue 27

Tuswan Tuswan et al. / Procedia Structural Integrity 27 (2020) 22–29 Tuswan et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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The number of assumptions within the framework of the debonding modeling has been previously explained. The free vibration analyses are performed using linear perturbation load step within ABAQUS software, where the Lanczos iteration method for eigenvalues extraction is used (ABAQUS, 2014). Influences of debonding presence on the modal characteristics are assessed by comparisons of dynamic responses between a healthy stern ramp/door and debonded model. The commercial finite element code, ABAQUS/Standard, is employed to obtain the natural frequencies and mode shapes of the models. The procedure for finite element (FE) simulation can be divided into three steps: (1) preprocessing which involves modeling the geometry of the structures, meshing and assembling of the mass and stiffness matrices; (2) A linear perturbation analysis step is created, and the frequency is extracted using the Lanczos solver. (3) The natural frequencies and mode shapes are obtained using the post-processing module. In the finite element model discretization of the models, the sandwich panel can be modeled using the layer-wise solid/shell element (Krueger and O’Brien, 2001). The use of shell elements can reduce the number of degree -of freedoms (DOF). However, the stress in the thickness direction can be better modeled using solid elements. So, the faceplate is modeled using the eight-node quadrilateral shell element (SC8R) with reduced integration, and the core material is modeled using the eight-node hexahedral element (3D8I) with incompatible modes. The longitudinal and transverse stiffeners are modeled using the eight-node quadrilateral shell element (SC8R) with reduced integration. The boundary condition applied to the model is C-F-C-F (clamped in after and fore stern/ ramp door, and free in the side structure). Mesh convergence analysis is conducted to verify the correctness of the model. In the finite element discretization, a finer mesh commonly results in a more accurate solution. However, as a mesh is made finer, the computation time will increase. One method to obtain a mesh that thoroughly balances accuracy and computing resources is by performing a mesh convergence study. The mesh convergence in the healthy stern/ ramp door model is analyzed. The mesh convergence study is carried out by investigating free vibration analysis to obtain the natural frequency of the first bending mode. The step is by creating a mesh using the fewest and reasonable number of elements and analyze the model. Then, recreate the mesh with a denser element distribution, re-analyze it, and match the obtained results to those of the previous mesh. Keep increasing the mesh density and re-analyzing the model until the results converge satisfactorily. Therefore, several mesh sizes are used to get the optimum mesh sizes. The mesh sizes are analyzed between 0.1 m and 0.03 m. The mesh element size 0.05 m with the number of elements and nodes 210,861 and 279,157, respectively, is used. Good agreement indicating successful modeling of eigen vibration problem can be recognized. Therefore, it validates the correctness of the model discretization used in this analysis. This section discusses the effect of debonding shapes in the stern/ ramp door analyzed in the first ten-mode. Both “with” and “without” contact conditions, as previously stated, are compared. All the model geometry, boundary condition, and material properties are like the models used in the mesh convergence study. The free vibration analysis using the Lanczos iteration method for eigenvalues extraction is applied. The frequency extraction procedure is to perform eigenvalue extraction and to calculate the natural frequencies and the corresponding mode shapes. Fig. 4 demonstrates the comparison of natural frequencies of intact and debonding models with spring contact modeling with different debonding shapes analyzed in the first ten-mode. As observed from Fig. 4, damage causes a decrease in natural frequency, especially in the square and circular debonding shape, but it seems there is no significant natural frequency decrease in the through-the-length, and through-the-width debonding. Natural frequency is affected by the presence of the circular and square imperfection and significantly alter in higher modes. One can see that the effect of debonding shapes, generally, has no regularity on the changes in the natural frequencies (Burlayenko and Sadowski, 2011b). 3. Numerical result of free vibration analysis 3.1. Model validation 3.2. Effect of debonding shape