جستجوی مقالات مرتبط با کلیدواژه « isogeometric analysis » در نشریات گروه « مکانیک »

In this paper, Isogeometric analysis (IGA) based on nonuniform rational B-splines (NURBS) is developed to study the free vibration analysis of the perforated plates with different open hole shapes and hole patterns. In this way, the governing equilibrium equations of perforated plate and strain-displacement relations are obtained using the first-order shear-deformable plate theory. The optimal number of control points and the order of the NURBS basis functions are determined to perform physical geometry related to perforated plate geometry. The eigenvalue equations with linear stiffness are established using the weak form of motion equations, energy method and Hamilton principle. The vibrational frequencies and corresponding mode shapes of the perforated plate is derived from governing eigenvalue equations. The results of linear vibrations of plate with central hole are validated considering the previously reported data and finite element analysis, which showed a good agreement. Thereafter, the influence of hole size and shape are explored on the linear vibrations of the plate with hole in same hole area ratio. Further, the effect of the triangular and rectangular pattern under the fully clamped and simply boundary conditions is presented.

In this paper, the isogeometric analysis of shell structures along with the optimal method for accurate calculation of nodal vectors is proposed. The Nurbs surface with maximum regularity is used for shell mid-surface description. According to the Reisner- Mindlin hypothesis, the director vectors at control points are needed for the interpolation of the rotations. The calculated nodal direct vectors must lead to exact interpolated director vectors on the shell surface. Hence, a method has been proposed in which the components of director vectors at control points are obtained by solving a system of equations on the whole patch. The system of equations is formed using known values of direction vectors at the Greville points. The accuracy of the proposed method has been investigated by using the results of the most common problem in shell analysis. Convergence behavior for displacement at the loading points has been studied in all solved problems for different order of NURBS and net of control points. The deformation results show better convergence behavior with increasing the regularity and order of NURBS. The knot averages are in a one-to-one correspondence with control points. Thus, the system of equations on these points leads to a unique solution for the nodal direction vectors, and the time to solve equations is significantly reduced.

In this research, an approach based on the isogeometric method is developed to study the free vibration behavior of functionally graded carbon nanotubes reinforced composite skew folded plates. In this method, non-uniform rational B-splines basis functions are used for approximation of the geometry as well as the displacement field. The plates are reinforced by single-walled carbon nanotubes which are assumed to be graded through the thickness direction with different distribution patterns. The effective mechanical properties of composite skew folded plates are captured by the modified rule of mixtures approach. Modeling of the skew folded plate is accomplished by two non-uniform rational B-splines patches which is one of the strengths of the research. The equations of motion of each patch are derived based on classical plate theory and then are discretized using non-uniform rational B-splines basis functions. The final form of the discretized equations is generated after the transformation of the element matrices of each patch and then applying the continuity conditions along the boundary of the patches with the aid of the bending strip method. Afterward, several numerical examples are provided to prove the accuracy and reliability of the proposed formulation. The results exhibit that the present approach can precisely predict the natural frequencies of skew folded plates with a low computational cost. Eventually, a set of new results are presented for different geometrical and material parameters of the skew folded plate.

A method for error estimation of isogeometric analysis of plane stress problems which is the based on stress recovery and using the super convergent properties of the Gauss points، has been already introduced. This paper is devoted to the development of the method and study of the effects of these supercovergent points on the solution improvement and error estimation of axisymmetric problems by the isogeometric analysis method. It is concluded that by using these optimal points for stress recovery and error estimation by isogeometric analysis a considerable improvement is attained.