As an innovative point of this work, the auxiliary functions are introduced to eliminate all the relevant discontinuities with the displacement and its derivatives at the boundaries and to accelerate the convergence of series representations.
The polynomial function is introduced to take all the relevant discontinuities with the original displacement and its derivatives at the boundaries and the Fourier series now simply represents a residual or conditioned displacement that has at least three continuous derivatives.
Regardless of boundary conditions, the displacements of each layer are expanded as the linear combination of a standard Fourier series and closed-form functions introduced to eliminate all the relevant discontinuities with the displacements and derivatives at the edges.
Regardless of boundary conditions, the displacements of each layer are expanded as the linear combination of a standard Fourier series and closed-form functions introduced to eliminate all the relevant discontinuities, ensure and accelerate the convergence of the series expansions.
Each of displacements of the plates, regardless of boundary conditions, is expanded as a three-dimensional (3-D) Fourier cosine series supplemented with closed-form auxiliary functions introduced to eliminate all the relevant discontinuities with the displacements and its derivatives at the edges.
Each of the shell displacements, regardless of boundary conditions, is constructed as a standard Fourier cosine series supplemented with auxiliary functions introduced to eliminate all the relevant discontinuities with the displacement and its derivatives at the edges and accelerate the convergence of series representations.
Under the current framework, each of the shell displacements, regardless of boundary conditions, is expanded as a standard Fourier cosine series supplemented with closed-form auxiliary functions introduced to eliminate all the relevant discontinuities with the displacement and its derivatives at the edges and accelerate the convergence of series representations.
Furthermore, other Authors have used the full series (i.e. before and after the change) for analysis of farm income without reporting relevant discontinuities in the data series (Henke and Salvioni 2013).
The ability to identify relevant parameters and provide discontinuity characteristics could eventually serve as basis for civil engineers in making efficient decisions regarding concerns on concrete structure.
To become more policy-relevant the notion of discontinuity needs to be embedded in scenario methodology on various levels; epistemological, analytical, contextual, and procedural [13].
