Derivation of Explicit Augmented Spline Finite Strip Matrix Using Mixed Formulation For Plate Bending

Abstract

Although Spline finite strip method for the analysis of plate bending based on a mixed variational formulation principle , using a variety B-Spline series as interpolation function was widely used in researches , the explicit form of the Augmented Matrix nowhere given. This leads to some difficulties concerning the verification and understanding the published results. The main objective of this paper is to introduce this matrix in abbreviated size through a detailed review of the mixed formulation for different spline finite strip models. The derived matrix will be helpful subject of research future work as it is examined by the time, reveals a very good accordance results compared with the analytical and published solutions of different plate bending problems as the reader can verified.

Plate Bending Spline Finite Strip Models Using Mixed Formulation and Combined Spline Series

“…Since the spline finite strip method based on stiffness formulation was introduced in the early eighties, although it is capable of solving many engineering problems such as plate bending [1]- [3], vibration [4] [5], and buckling [6] [7], it is subjected to many improvements such as the mixed formulation technique based on variational principles, where the authors previous work leads to the availability of the explicit form of the Augmented Matrix of such formulation [8], consequently the branch of improvement of interpolation functions take the place. This paper is aimed at studying several B-spline modifications for their applicability in modeling of engineering problems which frequently requires the restraint of a number of interior nodes as well as describes the construction of combined splines (CB-spline) as interpolation function in order to overcome on some difficulties of conventional spline finite strip plate bending, and thus a new type of CB-spline interpolation is presented.…”

Euler-Bernoulli and Timoshenko Beam Theories Analytical and Numerical Comprehensive Revision

“…A simplified detailed discussion of weakening such integrals can be found in first-author et-al. previous works[24]-[27], then the weak forms of these governing equations are: suggests linear interpolation functions for each of the field variables 𝑀 𝑥 , 𝑎𝑛𝑑 𝑤, in terms of deflection and moment at nodal values 𝑤 𝑎 , 𝑤 𝑏 & 𝑚 𝑥𝑎 , 𝑚 𝑥𝑏 as:…”