A B S T R A C T In this work the differential quadrature method is applied to first-order shear deformable composite plates having a through-width delamination. The semi-layerwise modeling technique is applied to capture the delamination, the governing equations of the plate are presented based on some previous works. The methods of two and four equivalent single layers are applied to provide some numerical results. In this paper four cases with two different lay-ups are applied depending on

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... position of delamination. The plates are subjected to a concentrated transverse force in the middle in each case. First, the convergence of deflection by the differential quadrature method is compared to that by analytical and spatial finite element models for simply-supported plates. It was recognized that the solution deviates between an upper and lower bounds. The convergence of mode-II and mode-III energy release rates was also investigated and it was found that the method of two equivalent single layers provides a "peak-valley" oscillatory phenomenon of the mode-II component. Second, the differential quadrature method using four equivalent single layers was applied to fully clamped plates with delamination. The upper and lower bounds the solution deviates within were observed, moreover the importance of proper grid structure was highlighted in order to avoid the waviness of the mode-III energy release rate. Laminated composites are primary parts of engineering structures. Composite materials can be designed to satisfy the requirements of the actual structure from the viewpoint of material properties, strength, lifetime and among others the dynamic behavior. The most essential fields that composite materials are applied within are space-and aircrafts, ships, car bodywork construction, submarines, pressure vessels and satellites [1] [2] [3] [4] [5] [6] . The heterogeneous structure of composites on the other hand make them susceptible to different type of damage modes. One of them is the interlaminar fracture or simply called delamination [7] [8] [9] [10] [11] [12] [13] . This work is essentially dedicated to the modeling of delaminations using mechanical models. The development of mechanical models is quite important in order to be able to predict the behavior of the structures and to estimate the lifetime of the material. The common aspect of the mentioned examples is that each is constructed using either thin-or thick-walled beam, plate and shell components. The literature offers a wide variety of beam, plate and shell theories, and thus, the user can choose the right theory in accordance with the design aspects. The classical laminated (CLPT) and the first-order shear deformation (FSDT) plate theories are well-known in the society of composite researchers [14, 15] . The classical theory has limited possibilities especially for thick laminates and sandwich structures. In such cases transverse shear plays a very important role, and at least the FSDT theory should be applied [16] [17] [18] [19] [20] . If the transverse shear is more severe, then other higher-order E-mail address: szeki@mm.bme.hu. theories can be chosen, such as the second-order (SSDT) [21, 22] , thirdorder (TSDT) and Reddy third-order [16, 17, [23] [24] [25] shear deformation plate theory, as well as other higher-order shear deformation theories (HSDT) [26] [27] [28] [29] [30] [31] . Further developments can be achieved by adding the transverse stretching term to the displacement field [24, [32] [33] [34] [35] [36] . These are the so-called equivalent single layer (ESL) theories dealing with only one layer having stiffness properties determined by the physical lay-up of the structure. If the interlaminar stresses are required more accurately in the ply level, then the layerwise theories (LWT) and models can be applied. Many layerwise models are available in the literature [37] [38] [39] [40] [41] [42] [43] , most of them are based on the expansion of FSDT, i.e. the displacement function is piecewise linearly distributed in each layer satisfying displacement continuity as well. Apparently, the second-and third-order theories can be extended too to develop layerwise models. The partial LWTs capture only the in-plane displacement in the form of a Taylor series, but the deflection is the same in each layer. The fully layerwise models are based on the expansion of all three displacement field components. The LWTs have been overviewed recently in [37] and [44] . In accordance with the former review papers LWTs are classified into the displacement-based and the mixed theories according the selection of solution variables. From the point of view of the displacement field assumptions in the thickness direction, the LWTs also can be divided into two groups: discrete layerwise methods (DLWM)