Quadratic finite element/strip with generalized degrees of freedom and their application

This paper presents a quadratic finite element with generalized degrees of freedom (GDOF) and a quadratic finite strip with GDOF based on the principle that the local displacement fields of elements should be compatible with the global displacement field of the corresponding systems. Firstly, a global displacement field is developed using quadratic B-spline functions. Secondly, local displacement fields of elements and strips are constructed, employing multi-term interpolation polynomials of second degree. Making the local displacement fields of elements and strips be compatible with their corresponding global displacement fields, respectively, models of the finite element with GDOF and the finite strip with GDOF are accordingly generated. On the other hand, the quadratic B-spline function is convenient to derive the explicit form of characteristic equations for computing model because of its lower order, and accordingly simplifies the computation, compared with cubic and quintic spline functions. Several numerical examples demonstrate the accuracy, simplicity and versatility of the present element and strip in the analysis of thin-walled structures.