---

One of the most remarkable achievements of finite element method is introducing isoparametric elements. Although these elements are able to use in numerous applications, the lower order isoparametric elements make some difficulties such as shear locking, volumetric locking and hourglass. These issues may improve with an increase in the number of the elements or by increasing the order of the elements, which increases the computational time. Therefore for solving these problems, using the lower order elements with incompatible modes, which enhances accuracy and reduces the computational time, could be considered as an alternative solution option. The aim of this paper is to study the effect of using the incompatible elements on the elastoplastic behavior of isotropic plates and beams under uniform axial and bending loadings. For this purpose, 3D standard elements with eight and twenty nodes and incompatible eight-node elements are used in modeling the 3-D case studies. Besides, the 2D standard elements with four and eight nodes and incompatible ones with four nodes are employed to analyze the 2-D plane stress problems. The obtained results show that using 3D incompatible elements achieves the faster rate of convergence in the solution procedure for obtaining the displacement components and also makes significant run-time reduction. However, there are not any remarkable differences between the obtained plastic Von-Mises stresses using 2D standard and incompatible elements.

---

In this study, the buckling and postbuckling behavior of composite laminates with piezoelectric layers subjected to compressive in-plane loading have been investigated. The effects of coupled electro-mechanical field on the postbuckling and bifurcation point in cross-ply and general lay-up sequences have been studied using layerwise theory (LWT). The LWT used in this study for analyzing the piezo-composite laminate is based on the assumptions of the first order shear deformation theory (FSDT). In order to obtain the equilibrium equations, the principle of minimum potential energy has been employed. The obtained nonlinear equilibrium equations have been solved using Newton-Raphson iterative algorithm. Furthermore, the three dimensional finite element analysis has been performed to examine the accuracy of the results obtained using the proposed method. The obtained analytical results are in good agreement with those achieved through the finite element analysis. Obtained results showed that, location of the piezoelectric layers have significant effect on the buckling and postbuckling behavior of the composite plates. Moreover, number of degrees of freedom which is used in proposed method are less than finite element method which, decreased the computational time cost.