Dynamic Instability in Shallow Arches under Transversal Forces and Plane Frames with Semirigid Connections

Abstract

Structural engineering demands increasingly lighter systems, which can cause instability problems and compromise performance. A high slenderness index of a structural element makes it susceptible to instability. It is important to understand the problem, the limits of stability, and its postcritical behavior. An example that can occur in collapsed arches under a cross load is the dynamic snap-through behavior, where the structure in a given equilibrium condition jumps to a new remote equilibrium setting, causing usually sudden curvature. The semirigid connections are a source of physical nonlinearity and can influence the overall stability of the structural system, in addition to the distribution of stresses in the same system. Conventional approaches make use of static considerations. However, instability problems are inherently evolutionary processes, so a transient analysis is necessary for a complete description of structural behavior. The present work evaluates the geometrically nonlinear dynamic behavior of collapsed arches subjected to transverse force and plane frames with semirigid connections. The time domain responses, via Newmark's Method and positional formulation of the Finite Element Method, were obtained in terms of displacements, velocities, acceleration, and phase diagrams.

Influence of Retardation Time on Viscoelastic Behavior of Plane Beams Modeled by the Nonlinear Positional Formulation of the Finite Element Method

“…Different numerical formulations have been developed to analyze the viscoelastic behavior of solid materials, as demonstrated in the works of Chen [1], Aköz and Kadioǧlu [2], Beijer and Spoormaker [3], Zheng et al [4], Mesquita and Coda [5], Galucio et al [6], Bottoni et al [7], Payette and Reddy [8], Panagiotopoulos et al [9], Latorre and Montáns [10], dos Santos Becho et al [11], Carniel et al [12], Oliveira and Leonel [13], Pascon and Coda [14], Rabelo et al [15], and Fernandes et al [16]. is interest is due to the need for modeling behavior of unconventional materials and the more complex and realistic analyzes of structures and structural components.…”

“…e creep behavior is related to the gradual evolution of strains over time when the solid is submitted to a constant stress state. us, from equation (16) and considering the constant stress state σ � σ 0 , one has…”

“…us, structural engineering aims to address the demands for technological advances in the most diverse areas, such as infrastructure, civil construction, mechanical industry, aerospace industry, and others. Part of these studies are related to the analyses of structures with viscoelastic behavior adopting stress-strain relation deduced from rheological models, as demonstrated in the works of Aköz and Kadioǧlu [2], Mesquita and Coda [5], Panagiotopoulos et al [9], dos Santos Becho et al [11], Carniel et al [12], Oliveira and Leonel [13], Pascon and Coda [14], Rabelo et al [15], and Fernandes et al [16]. ese rheological models are schematic representations that combine elastic and viscous elements to obtain a physical interpretation of stress-strain relationships.…”

“…It is worth mentioning that part of these studies uses the positional formulation of the finite element method to describe the viscoelastic behavior, as demonstrated in the works of dos Santos Becho et al [11], Pascon and Coda [14], Rabelo et al [15], and Fernandes et al [16]. e use of such a formulation is justified by the capacity and simplicity of its application in the analysis of nonlinear problems as highlighted in Coda and Greco [17] and Greco and Coda [18].…”

Numerical-Computational Model for Nonlinear Analysis of Frames with Semirigid Connection

“…A numerical approach based on the member discrete element method to investigate static and dynamic responses of steel structures with semirigid joints was presented by Ye and Xu [14]. Fernandes et al [15] evaluated the geometrically nonlinear dynamic behavior of collapsed arches subjected to transverse force and plane frames with semirigid connections. e performance of base-isolated steel structures having special moment frames was assessed by Rezaei Rad and Banazadeh [16].…”