One of the remarkable concerns in Shallow arches’ behavior under lateral loading is snap-through, aphenomenon which can make the structure collapse or displace to another stable configuration.Introducing functionally graded materials in recent years has led to some interesting results, forinstance, using functionally graded materials in Shallow arches can produce structures with favorablestability properties. In this work, we investigate dynamic stability of the pined-pined functionallygraded sinusoidal Shallow arch under impulsive loading. Material properties vary through the thicknessby power law function. Nonlinear governing equations are derived using Euler-Bernoulli beamassumption and equations of motion are expressed by a nonlinear differential-integral equation. Thesolution utilizes a Fourier form of response. The procedure to analyze dynamic stability followed hereuses total energy of the system and Lyapunov function in the phase space. We find the stable regionagainst dynamical snap-through under material properties’ variation in the thickness direction ofShallow arch. We also proceed to find the sufficient critical load in order to make the dynamical snapthrough occur. The results are analyzed in detail and illustrated in some diagrams.

In this work, the nonlinear buckling and post-buckling behavior of Shallow arches made of Shape Memory Alloy (SMA) is investigated. arches are susceptible to large deflections, due to their slenderness, especially when the external load exceeds the serviceability limit point. Beyond this, loss of stability may occur, the famous snap-through buckling. For this reason, curved beams can be used in passive vibration control devices for seismic response mitigation, and the geometrically nonlinear analysis is needed for the accurate prediction of their response. Thus, in this research effort, the assumptions of the Euler-Bernoulli beam theory are considered, and the Von Karman strain field is employed to account for large deflections. The formulation of the problem is displacement-based regarding the axial (tangential) and transverse (normal) displacements, while the two governing equations are coupled and nonlinear. In order to introduce the SMA constitutive law, the stress-strain experimental curves described in the literature are employed together with a fiber approach at specific control cross-sections along the beam. The numerical solution of the longitudinal problem is achieved using the Analog Equation Method (AEM), a Boundary Element Method (BEM) based technique, and the iterative procedure is based on a Newton-Raphson scheme by using a displacement control algorithm to trace the fully nonlinear equilibrium path and overcome the limit points. Several representative examples are studied, not only to validate the proposed model but also to investigate the nonlinear buckling and post-buckling of SMA Shallow arches.

Analysis of stability in arch structures is a well-known fact in the conservation of historical monuments, stabilizing efforts, and the design of vernacular and rural structures. Therefore, the authors of this paper are set to explore and compare the threshold values of the seismic stability of three Persian arches, i. e., tokhm-e morqi, morabbaʿ , and panj-o-haft-e-tond. This experimental research uses geometrical analysis and physical models to find the threshold values for the seismic stability of these arches. Analysis of the arches is performed for different thickness-to-span ratios within the “ limit state analysis” framework, using “ thrust line analysis” with parametric modeling which offers a rigorous and rapid investigation. The results are then compared with the behavior of physical models. The thrust line analysis results show that the seismic stability of these arches, compared to one another, increases by increasing the thickness-to-span ratio and decreasing their rises. The physical models verify these results but show lower threshold values for seismic stability of the arches. So, the effective thickness of the arches must be considered in the analysis. Besides answering a practical problem, this paper gives an insight into the structural behavior of arches.

arches, vaults and domes are common features in the cultures of old civilizations. They were usually made of sun-dried bricks, fired bricks or stones with different types of mortar. The majority of these components are vulnerable to seismic effects. To present a viable study on their seismic vulnerability, all the factors influencing their behavior need to be investigated. In this paper, the construction materials used and the structural features of these elements are briefly described. Furthermore, the different aspects of using numerical methods for analyzing these elements are discussed. Finally, measures needed to improve their resistance are suggested.