On Convergence of a Three-layer Semi-discrete Scheme for the Nonlinear Dynamic String Equation of Kirchhoff-type with Time-dependent Coefficients

This paper considers the Cauchy problem for the nonlinear dynamic string equation of Kirchhoff-type with time-varying coefficients. The objective of this work is to develop a temporal discretization algorithm capable of approximating a solution to this initial-boundary value problem. To this end, a symmetric three-layer semi-discrete scheme is employed with respect to the temporal variable, wherein the value of a nonlinear term is evaluated at the middle node point. This approach enables the numerical solutions per temporal step to be obtained by inverting the linear operators, yielding a system of second-order linear ordinary differential equations. Local convergence of the proposed scheme is established, and it achieves quadratic convergence concerning the step size of the discretization of time on the local temporal interval. We have conducted several numerical experiments using the proposed algorithm for various test problems to validate its performance. It can be said that the obtained numerical results are in accordance with the theoretical findings.Comment: 31 pages, 13 figures, 11 table

Buildings and Structures under Extreme Loads II

Exceptional loads on buildings and structures are known to take origin and manifest from different causes, like natural hazards and possible high-strain dynamic effects, human-made attacks and impact issues for load-bearing components, possible accidents, and even unfavorable/extreme operational conditions. All these aspects can be critical for specific structural typologies and/or materials that are particularly sensitive to external conditions. In this regard, dedicated analysis methods and performance indicators are required for the design and maintenance under the expected lifetime. Typical issues and challenges can find huge efforts and clarification in research studies, which are able to address with experiments and/or numerical analyses the expected performance and capacity of a given structural system, with respect to demands. Accordingly, especially for existing structures or strategic buildings, the need for retrofit or mitigation of adverse effects suggests the definition of optimal and safe use of innovative materials, techniques, and procedures. This Special Issue follows the first successful edition and confirms the need of continuous research efforts in support of building design under extreme loads, with a list of original research papers focused on various key aspects of structural performance assessment for buildings and systems under exceptional design actions and operational conditions