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Nonlinear dynamic analysis of RC columns subjected to lateral impact loads
Published in Chunwei Zhang, Gholamreza Gholipour, Concrete Structures Subjected to Impact and Blast Loadings and Their Combinations, 2022
Chunwei Zhang, Gholamreza Gholipour
In this study, a container ship with a weight of 10,000 tons is considered as the impacting vessel on the piles' cap level of pier-4 as shown in Figure 4.16. Figure 4.17 shows the details of the FE model of the ship including the internal stiffeners, outer plates in the bow portion which are modeled using four-node shell elements, and the stern portion is modeled using eight-node solid element in LS-DYNA. According to the previous studies in the literature [53, 54], the ratio of length to thickness of the FE elements used for the ship bow is selected in the range of 8–10 to capture the converge results. Totally, 39,292 and 48,816 elements are used for internal stiffener plates and outer plates in ship bow portion, respectively. A series of numerical mesh size convergence tests were carried out for FE model of the ship to reach the reliable ship-pier collision results. In these tests, the ship bow collides with a rigid wall with different mesh sizes as shown in Figure 4.18. It was found that impacted wall with a mesh size of 200 mm can capture the converge results. Therefore, the mesh size of 200 mm is selected for FE model of the impacted pier at the impact zone on the piles' cap and for the pier columns. The calibration of contact force versus the crushing depth of the ship bow during the collision with a rigid wall with a mesh size of 200 mm is shown in Figure 4.18a and b. The results from the present study are compared with those from the previous work [55, 56] and the standard codes [57–59]. The ratio of longitudinal reinforcements for all piers is considered around 2–4%. By considering the minimum requirements according to standard codes [45], the space between the transverse reinforcements is 300 and 150 mm in the columns and the beam member, respectively. In order to simulate the interaction between the concrete and reinforcements, a coupling algorithm called CONSTRAINED_LAGRANGE_IN_SOLID is used in LS-DYNA. To simulate the contact and interactions between the separate components and to prevent from any penetrations of the elements, several contact algorithms are used in LS-DYNA, which are tabulated in Table 4.3.
Post-quake structural damage evaluation by neural networks: theory and calibration
Published in European Journal of Environmental and Civil Engineering, 2019
Hichem Noura, Ahmed Mebarki, Mohamed Abed
where Dmin and Dmax are the lowest and the highest component damage values, respectively.Selection of neurons number (h) and hidden layers number (l): Several authors have reported consensual and empirical results about the optimal hidden layers number and neurons number in each layer (Jordan, 1995; Moré, 1978; Swingler, 1996). As we have investigated three options for the set of governing (input) parameters, a sensitivity analysis has been performed in order to find the best neurons number (h) in each hidden layer according to series of convergence tests proposed by various studies (Akaike, 1992; Cybenko, 1989; Funahashi, 1989; Schwarz, 1978). For the set of buildings under study, the results show that the optimal value corresponds to h = n, i.e. h = 4 or 8 when the global structural damage is explained by a set of 4 or 8 input variables, respectively, see Equations (1) and (2). The sensitivity analysis has also shown that the optimal number of hidden layers is l = 1 (Hornik, 1991).Hidden layers - Inputs combination and intermediate neural results: Each neuron among the h neurons, in the intermediate layer, adopts combination of the normalised input parameters. Thus, for the linear combination which is adopted usually, the j-th neuron generates the j-th component Xj (j = 1 … h), (McCulloch & Pitts, 1943):
Dynamic response of a functionally graded cylindrical tube with power-law varying properties due to SH-waves
Published in Waves in Random and Complex Media, 2021
Ning Zhang, Yu Zhang, Denghui Dai
To determine a sufficient truncation number N of the series solution, convergence tests are first conducted in terms of DSCFs. Figure 2 shows the variation of the DSCFs with N at three representative positions on the inner tube surface. Only the results for the largest dimensionless frequency η = 4 used herein are displayed because it takes the most terms of series for the solution to reach convergence. One can observe that the DSCF at each position converges to a fixed value for N > 20. For conservative reasons, N = 50 is adopted for the high accuracy of the results hereafter.