mohammad rezaiee-pajand

For dynamic modal analysis of the gravity dams, it is required to solve the non-symmetric eigenvalue problem which is a time-consuming process. This paper aims to propose a new procedure for this purpose. In this novel method, there is no need to solve the non-symmetric coupled eigenproblem. Instead, two novel eigenvalue problems are formulated and solved. They are simultaneously applied for dynamic modal analysis of concrete gravity dams. They represent the cubic-symmetric forms of the respective non-symmetric Eigenvalue problem, and they are entitled “cubic ideal-coupled eigenproblems”. Moreover, it is proved that the decoupled and ideal-coupled schemes presented in the previous works can be considered as special cases of the current more general procedure. For solving the aforesaid cubic eigenproblems, the classical subspace algorithm is generalized. To assess the accuracy of the suggested technique, it is employed for the dynamic analysis of two well-known benchmark gravity dams in the frequency domain. The dam crest responses are calculated under upstream and vertical excitations for two different wave reflection coefficients. Then, the obtained results are compared with those of the decoupled and ideal-coupled approaches. Findings corroborate the fact that the authors' formulation is more accurate than the other two aforesaid tactics under all practical conditions.

In this paper, an explicit family with higher-order of accuracy is proposed for dynamic analysis of structural and mechanical systems. By expanding the analytical amplification matrix into Taylor series, the Runge-Kutta family with  stages can be presented. The required coefficients ( ) for different stages are calculated through a solution of nonlinear algebraic equations. The contribution of the new family is the equality between its accuracy order, and the number of stages used in a single time step ( ). As a weak point, the stability of the proposed family is conditional, so that the stability domain for each of the first three orders ( 5, 6, and 7) is smaller than that for the classic fourth-order Runge-Kutta method. However, as a positive point, the accuracy of the family boosts as the order of the family increases. As another positive point, any arbitrary order of the family can be easily achieved by solving the nonlinear algebraic equations. The robustness and ability of the authors’ schemes are illustrated over several useful time integration methods, such as Newmark linear acceleration, generalized-𝛼, and explicit and implicit Runge-Kutta methods. Moreover, various numerical experiments are utilized to show higher performances of the explicit family over the other methods in accuracy and computation time. The results demonstrate the capability of the new family in analyzing nonlinear systems with many degrees of freedom. Further to this, the proposed family achieves accurate results in analyzing tall building structures, even if the structures are under realistic loads, such as ground motion loads.

The importance of geometric and material nonlinear analysis in trusses is not deniable. Furthermore, everyone knows the importance of closed-form solution to the behavior of structures. However, the solution volumes make this type of analysis impossible or very difficult for most structures. Closed-form solution only for a few simple trusses, with geometric and material nonlinearities, can be obtained. Elastic analysis of trusses is widely performed by the methods, such as, the finite element scheme. So far, researchers have proposed many approaches for truss nonlinear analysis. New techniques are validated by the benchmark problems. In this view, it is important to have an explicit solution for this purpose. In this paper, some simple two and three-dimensional trusses are analyzed analytically. This study considers both large deformations with elastic-plastic behavior simultaneously. The behavior of material is assumed to have a bilinear diagram. The strain energy function is obtained in terms of the Green strain. Equilibrium equations are satisfied by minimizing total energy. At the point, in which determent of the tangent matrix becomes zero, structural instability is found. The load-displacement graph is obtained by analyzing the strain of the truss members in the stable range of the equilibrium path. It is important to know that the multi-relational function of the equilibrium path of each truss can be applied to test the accuracy of new nonlinear analysis techniques.

Performance-Based Plastic Design (PBPD) method has been recently developed to achieve the enhanced response of structures to earthquake. To reach this goal, several ways have been suggested. In this paper, the schemes of calculating base shear in the (PBPD) procedure will be studied. Two techniques of determining base shear will be used. The base shear of two steel moment frames will be found by these two processes. By using the difference between the input energy and the elastic strain energy to obtain the plastic energy, the plastic design is then performed to detail the frame members in order to achieve the intended yield mechanism and behavior. The inelastic seismic behaviors of the four frames were studied through nonlinear static and dynamic analyses. These two suggested techniques and their comparisons have not been proposed yet. This kind of plastic design has three main parts. Calculating base shear is the first and important portion. The second part consists of the member plastic design for flexible behavior. To design elastic members by using column trees is the third and last part. Throughout this study is devoted to present two methods for calculating base shear. The moment frames will be investigated in this article.

In this paper, a plane quadrilateral element with rotational degrees of freedom is developed. Present formulation is based on a hybrid functional with independent boundary displacement and internal optimum strain field. All the optimality constraints, including being rotational invariant, omitting the parasitic shear error and satisfying Fliepa’s pure bending test, are considered. Moreover, the static equilibrium equations are satisfied in this scheme. Authors’ element has only four nodes and twelve degrees of freedom. For the boundary displacement field, Alman’s second-order displacement function is employed. The validities of the proposed element are demonstrated by eleven numerical examples: thick curved beam, thin cantilever beam, Cooke’s skew beam, thin curved beam, cantilever beam with distortion parameter, high-order patch test, cantilever beam with five and four irregular mesh, Mc Neal’s thin cantilever beam and cantilever shear wall with and without openings. When utilizing the coarse and irregular meshes, numerical tests show the high accuracy, rapid convergence and robustness of the suggested element. Less sensitivity to distortion is another property of the new element.

In the last sixty yearsý, ýthe Dynamic Relaxation methods have evolved significantlyý. ýThese explicit and iterative procedures are frequently used to solve the linear or nonlinear response of governing equations resulted from structural analysesý. ýIn the first part of this studyý, ýthe common DR formulations are reviewedý. ýMathematical bases and also physical concepts of these solvers are explained brieflyý. ýAll the DR parametersý, ýi.eý. ýfictitious massý, ýfictitious dampingý, ýfictitious time step and initial guess are describedý, ýas wellý. ýFurthermoreý, ýsolutions of structural problems along with kinetic and viscous damping formulations are discussedý. ýAnalyses of the existing studies and suggestions for future research trends are presentedý. ýIn the second partý, ýthe applications of Dynamic Relaxation method in engineering practices are reviewed.

The most significant advances over the sixty years relative to the Dynamic Relaxation applications in structural engineering are summarized. Emphasized are given towards plates, form finding, cable structures, dynamic analysis, and other applications. The role of DR solver in the linear and non-linear analyses is discussed. This investigation is undertaken to explain the application of the solution technique to the static, dynamic and stability problems. The influence of the methods on the use of isotropic and composite materials, such as orthotropic and laminated ones, is briefly covered. Critical analyses and suggestions regarding future research and applications will be presented.

The main purpose of this paper is the nonlinear analysis of bending plates with the finite difference. Based on the variable damping, the dynamic relaxation technique will be utilized. In order to achieve proper convergence, the velocity, kinetic energy and two successive displacement ratio criteria are used. For various bending plate samples, the results of constant and variable damping are compared. Numerical examples show that the variable damping is better than the constant damping. However, author's scheme reduces the number of iterations and the time duration. The finite difference method is very sensitive to the choice of some factors. A slight change in the amount of these parameters will increase the number of iterations and the time duration. Moreover, sometimes the solution procedure is divergenced. Another goal of this article is presenting a brief review of the dynamic relaxation approach in solving the bending plates.

In this paper, two new quadrilateral elements are formulated to solve plane problems. Low sensitivity to geometric distortion, no parasitic shear error, rotational invariance, and satisfying the Felippa pure bending test are characteristics of these suggested elements. One proposed element is formulated by establishing equilibrium equations for the second-order strain field. The other suggested element is obtained by establishing equilibrium equations only for the linear part of the strain field. The number of the strain states decreases when the conditions among strain states are satisfied. Several numerical tests are used to demonstrate the performance of the proposed elements. Famous elements, which were suggested by other researchers, are used as a means of comparison. It is shown that these novel elements pass the strong patch tests, even for extremely poor meshes, and one of them has an excellent accuracy and fast convergence in other complicated problems.

It is aimed to minimize the structure response against the earth vibration by the use of the open loop control system. In such a control, only one predicting neural network is utilized, which estimates only the earth vibration. The neural network is instructed by some recorded acceleration data, and it is able to predict the acceleration variation for the subsequent step. The control force is equal to the product of the mass of each story to its next step acceleration. This control system leads to the approximate minimum response. Moreover, to guarantee the system stability, a linear controller is added to the system. The resulted mixed control system can assure the system stability and also has better performance. Finally, the effect of the structural mass variation on the control system is investigated. The findings show that the effect of the structural mass variation on the mixed control system is smaller than the one by the predicting neural network

Kani method is a simple and robust tactic for analysis of building frames، which was proposed on 1950s and has been progressed substantially، so far. In contrast to the moment distribution approach، this technique can take into account the lateral transitions as well as nodal rotations of frames simultaneously. Based on this ability، Kani method is a suitable and cheap strategy for analysis of frame structure with the lateral shift. In this paper، Kani technique is extended to analyze braced frames to withstand lateral forces. The proposed formulation is utilized to solve some numerical problems. For the sake of the comparison، the results are also checked by matrix structural analysis method.

Geometrical imperfections usually occur during fabrication and erection. Initial out-of-straightness is one of the most common types of these flaws. In this paper, the elastic tangent stiffness matrix of an initially curved beam-column element subjected to nodal forces and transverse member loads is derived. Second-order analysis of planar frames is carried out afterwards. The proposed method introduces a new function for explicit modeling of out-of-straightness imperfection and incorporates it directly into the element's stiffness matrix. In addition, the proposed technique uses only one element for each member and presents a single formulation for both tensile and compressive members. The obtained load-deflection curve is compared with those predicted by other methods and the effect of initial out-of-straightness imperfection is also discussed. Results of numerical examples indicate that initial out-of-straightness imperfection is less important if the stability of frame is controlled by second-order P-Δ effect. On the other hand, it can have a considerable effect on the behavior of structure when second-order P-δ effect is dominant.