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This article presents an analytical technique for determining the free vibration response of a rectangular tank. It is assumed that this structure has a flexible foundation and rigid walls. The effects of beneath soil are considered by using Winkler and Pasternak foundations. To verify the authors' responses, the finite element solutions are also compared with the analytical results. Additionally, a closed-form approximate relationship is provided in this research work to determine the first natural frequency of the tank resting on a deformable foundation. In order to find the effect of various parameters, such as the stiffness of the elastic foundation and tank dimensions, on the natural frequencies of this system, a sensitivity analysis is also carried out. [ABSTRACT FROM AUTHOR]

This paper deals with dynamic analysis of functionally graded beams on elastic foundation considering damping effect. It is assumed that the mechanical properties of the material vary along the beam thickness. The fourth-order differential equation is analytically solved by means Green's function method, and exact answer is achieved. Damping effect, which is an intrinsic property of structures with great influence on the forced vibration of mechanical systems is included in the analysis. However, due to difficulty involved, it is usually neglected in the analysis of structures. Furthermore, the effect of rotary inertia is considered in the problem formulations. Green's function method is a straightforward way to model physical problems subjected to arbitrary loads and affected by various parameters, such as, elastic foundation, damping, geometry and mechanical properties. It could be a unique solution to gain the exact answers via the superposition manner. To demonstrate the accuracy and efficiency of the presented solution, dynamic response of the beam under different harmonic loads is obtained and compared to available results in some cases. [ABSTRACT FROM AUTHOR]

It is aimed to propose a new triangular plane finite element to improve the accuracy and reduce the computational effort for analysis of plane structures. The suggested element is formulated by assuming an incomplete second-order strain field. It leads to an element free from shear parasitic error with lower sensitivity to the mesh distortion. Satisfying both equilibrium and compatibility equations in the strain field level results in 12 independent strain states. Accordingly, the suggested element has 12 degrees of freedom, which are allocated to six nodes. Although the suggested element has the geometry and number of degrees of freedom same as the well-known linear strain triangular element, but its accuracy and efficiency are much better than many of the available high-performance membrane elements. The selected geometry provides the opportunity to simply include the presented element in the general finite element analysis software. After evaluation of the element performance using basic benchmark problems, to demonstrate the efficiency of the proposed formulation in comparison with widely used finite elements, different shear and retaining wall structures are analyzed by the developed element. The attained results for even coarse meshes prove higher accuracy and efficiency of the developed element in computation of displacements and stresses. Another advantage of the proposed element in comparison with the other available robust finite elements is its simple and straightforward formulation. [ABSTRACT FROM AUTHOR]

The recently emerged idea of incorporating higher-order strain or displacement discontinuities into standard finite element interpolations has triggered the development of robust techniques, which allow efficient modeling of large deflections and rotations. A number of studies on efficient elements with embedded high-order discontinuities, including mixed interpolation tensorial components (MITC) and assumed natural strain (ANS) elements, were published during the past decade. It was verified that local enrichments of the displacement and/or strain interpolation can enhance the responses of displacements and stresses by efficient models. The multitude of methods proposed in the literature calls for a comparative study that would present the diverse approaches in a unified framework, point out their common features and differences, and find their limits of applicability. In this regard, by proposing two robust triangular elements based on the higher-order strain field, mixed and strain-based approaches are compared. The strengths and weaknesses of individual formulations are elucidated by analyzing the convergence behavior. After determining the optimal condition, the nonlinear theoretical analysis of functionally graded (FG) shells has been performed by employing the weighted arc-length method. The equilibrium path for load-bearing factor versus post-buckling capacity, the error rate path and the residual force norm are also presented in different material and boundary conditions. [ABSTRACT FROM AUTHOR]

To design a steel shear wall, dynamics of stress concentration on the columns and beam under lateral loads is essential. Therefore, it has been suggested that the thickness of plates should be reduced as much as possible. In cases where a plate with low thickness is not available, this is compensated by using either low-yield-stress plate or by preparing some holes in the structure. Two objectives are pursued in this study, namely, the formulation of a new time integration method for evaluating structural seismic behaviour, and to discover the influences of the yield strength of the steel plate and openings on the wall. The results obtained indicate that the proposed scheme can accurately assess the seismic performance of structures. In addition, in the shear wall with low yield stress, where the steel plate has 5% and 10% openings, there are no significant differences between the outputs of widespread and concentrated openings. The behaviours of these two kinds of shear walls are approximately the same. [ABSTRACT FROM AUTHOR]

Various mathematical expressions have been proposed to evaluate or check the lapped length in spliced bars subjected to tension in reinforced concrete members. In this work, 284 tests on spliced bars were assessed in an attempt to improve the previous formulas, with the aim of proposing a new model to predict the lapped length, the transverse reinforcement spacing and the bond stress distribution in concrete beams with different compressive strengths. A genetic algorithm was used to optimise the proposed formulation. For both normal- and high-strength concrete, different bond-stress profiles were developed to predict the resistance provided by bonded embedment. The results clearly show that the proposed bond stress profiles lead to a more accurate evaluation of the lapped length in spliced bars than the expression proposed by the American Concrete Institute. [ABSTRACT FROM AUTHOR]

A six-node triangular shell element was developed to study the geometrically non-linear behaviour of open-section members. The present formulation is free from shear and membrane locking due to use of mixed interpolation of tensorial components scheme. Due to model thin-walled section, an improvement is considered to update the normal vectors of elements which are located at the angle between flange and web of section. In other words, an average of director vectors is employed for these elements in updating formulation. Moreover, the total Lagrangian formulation is employed to consider large displacement and rotation. An incremental iterative technique named generalised displacement control method is utilised to solve the governing equation. Several numerical examples are studied to illustrate the accuracy and predictability of the proposed formulation. [ABSTRACT FROM AUTHOR]

This study is dedicated to implement hygro-thermo-mechanical nonlinear analysis of curved thin and moderately thick shallow panels, in which Functionally Graded Materials (FGMs) are employed through the thickness. Based on the rule of mixture, three different patterns of FGMs, including power, exponential and sigmoid patterns are used in formulation. The distribution of porosity within the material is also considered to be uniform. Therefore, the elastic modulus and Poisson's ratio have a linear function. It is worth mentioning that thermal-dependency of materials is ignored, and it is assumed to be Thermal-Independent (TID). On the other hand, the shell structures are analyzed under the effects of hygro-thermal, mechanical and hygro-thermo-mechanical loads separately. It is aimed to obtain the post-buckling structural behavior, by considering large displacements and rotations. Some well-known benchmark problems are also considered to indicate the high accuracy, capability and performance of the proposed formulation in the nonlinear analysis of FG shells. Moreover, the influences of several parameters, such as, FGM patterns, thermal and moisture expansion coefficients and curvature ration of structure on the obtained results are accurately investigated. [ABSTRACT FROM AUTHOR]

This article deals with the free vibration analysis of a two-member nanogrid. First, the governing differential equations of flexural and torsional vibrations are found based on nonlocal elasticity theory. Second, the problem under study is formulated, considering the interaction of bending and torsion by direct method. It contains four partial differential equations and twelve boundary and compatibility conditions. Third, the problem is derived by using the variational method. Fourth, the problem at hand is analytically solved and natural frequencies of the structure are obtained. Finally, a finite element solution is developed for the problem at hand. A two-node six-degree-of-freedom nanogrid element is introduced. Comparison of both exact and numerical results shows an excellent agreement between findings via both methods. Findings can be served as benchmarks for future researchers. Communicated by Chandrika Prakash Vyasarayani [ABSTRACT FROM AUTHOR]

A new normal plane constraint for assessing the geometric non-linear behaviour of structures is proposed. In this procedure, the vector passing through a point placed on the equilibrium path and the iteration point is perpendicular to the locus of the iterative points. The capability of the suggested constraint equation was investigated numerically. To compare its abilities with other well-known techniques (the normal plane, cylindrical arc-length and updated normal plane methods), several planar and space trusses, plate and shells were analysed. The results proved the high accuracy and efficiency of the developed scheme. The powers of the methods in passing the limit points were also investigated. In addition, to assess the capabilities of the methods more accurately, they were all ranked based on the total number of increments and iterations required. [ABSTRACT FROM AUTHOR]

A new family of time integration methods is formulated. The recommended technique is useful and robust for the loads with large variations and the systems with nonlinear damping behavior. It is also applicable for the structures with lots of degrees of freedom, and can handle general nonlinear dynamic systems. By comparing the presented scheme with the fourth-order Runge–Kutta and the Newmark algorithms, it is concluded that the new strategy is more stable. The authors' formulations have good results on amplitude decay and dispersion error analyses. Moreover, the family orders of accuracy are m + 2 and m + 3 for even and odd values of m , respectively. Findings demonstrate the superiority of the new family compared to explicit and implicit methods and dissipative and non-dissipative algorithms. [ABSTRACT FROM AUTHOR]

The analysis of cable structures is one of the most challenging problems for civil and mechanical engineers. Because they have highly nonlinear behavior, it is difficult to find solutions to these problems. Thus far, different assumptions and methods have been proposed to solve such structures. The dynamic relaxation method (DRM) is an explicit procedure for analyzing these types of structures. To utilize this scheme, investigators have suggested various stiffness matrices for a cable element. In this study, the efficiency and suitability of six well-known proposed matrices are assessed using the DRM. To achieve this goal, 16 numerical examples and two criteria, namely, the number of iterations and the analysis time, are employed. Based on a comprehensive comparison, the methods are ranked according to the two criteria. The numerical findings clearly reveal the best techniques. Moreover, a variety of benchmark problems are suggested by the authors for future studies of cable structures. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to propose a new robust membrane finite element for the analysis of plane problems. The suggested element has triangular geometry. Four nodes and 11 degrees of freedom (DOF) are considered for the element. Each of the three vertex nodes has three DOF, two displacements and one drilling. The fourth node that is located inside the element has only two translational DOF. Design/methodology/approach: The suggested formulation is based on the assumed strain method and satisfies both compatibility and equilibrium conditions within each element. This establishment results in higher insensitivity to the mesh distortion. Enforcement of the equilibrium condition to the assumed strain field leads to considerably high accuracy of the developed formulation. Findings: To show the merits of the suggested plane element, its different properties, including insensitivity to mesh distortion, particularly under transverse shear forces, immunities to the various locking phenomena and convergence of the element are studied. The obtained results demonstrate the superiority of the suggested element compared with many of the available robust membrane elements. Originality/value: According to the attained results, the proposed element performs better than the well-known displacement-based elements such as linear strain triangular element, Q4 and Q8 and even is comparable with robust modified membrane elements. [ABSTRACT FROM AUTHOR]

To obtain proper stresses , three new triangular elements are formulated in this study. First, a complementary energy functional is used within an element for the analysis of plane problems. In this energy manifestation, the Airy stress function will be applied as a functional variable. Then, some basic analytical solutions are assigned for the stress functions. These trial functions are matched with each element number of degrees of freedom. The result is a number of equations with anonymous constants. Subsequently, according to the principle of minimum complementary energy, the unknown constants can be expressed in terms of displacements. Finally, this system can be rewritten in terms of the nodal displacement. In this way, three new triangular elements are formulated. To validate the results, extensive numerical studies are performed. The findings clearly demonstrate accuracies of structural displacements as well as stresses. [ABSTRACT FROM AUTHOR]

Summary: An effective and reliable approach to updating finite element (FE) models of real structures is to utilize a sensitivity‐based strategy. A challenging issue concerning the sensitivity‐based finite element model updating (FEMU) is to create a well‐established framework for updating the inherent structural properties of FE models under incomplete noisy modal data. When noise contaminates the measured modal parameters, another challenging issue stems from the ill‐posedness of the FEMU inverse problem. This article proposes an innovative sensitivity‐based FEMU strategy based on the combination of modal kinetic energy and modal strain energy for simultaneously updating the element mass and stiffness matrices of FE models. The great novelty of this strategy is to get an idea from the unconstrained optimization problem for the establishment of a sensitivity‐based FEMU framework. The correction of the element mass and stiffness matrices in a simultaneous way is another novelty of the proposed FEMU strategy. Moreover, new iterative and hybrid regularization methods under the Krylov subspace theory and bidiagonalization process are presented to solve the ill‐posed inverse problem of FEMU. The accuracy and reliability of the proposed methods are numerically validated by a two‐story concrete frame and a two‐span continuous steel truss along with some comparative analyses. Results demonstrate that the suggested sensitivity‐based strategy and regularized solution methods are influential and successful in FEMU under incomplete noisy modal data. [ABSTRACT FROM AUTHOR]

Dynamic Relaxation Method (DRM) is an explicit approach for solving the simultaneous systems of equations. In this tactic, the fictitious mass and damping are added to the static governing equations, and an artificial dynamic system is constructed. By using DRM for nonlinear analysis, the structural static equilibrium path is obtained. This outcome is extremely valuable, since it leads to the behavior of structures. Among the finding related to the structural static path are the critical and buckling points for nonlinear structures. In this paper, a new way for calculating the load factor is proposed by setting the external work zero. Mixing the dynamic relaxation scheme with external work technique has not been formulated so far. In all incremental-iterative methods, the load factor increment sign should be determinated by extra calculations. This sign leads to increase or decrease of the load increment. It is worth emphasizing that sign of the load factor increment changes at the load limit points. Therefore, the sign determinations are required in the common work control methods. These disadvantages are eliminated in the proposed algorithm. In fact, the suggested load factor depends only on the Dynamic Relaxation (DR) fictitious parameters. Besides, all DR calculations are performed via vector operation. Moreover, the load factor is calculated only by one formula, and it has the same relation in the all solution processes. In contrast to the arc length techniques, which requires the sign determined, the proposed scheme does not need any sign finding. It is shown that author's technique is quicker than the other dynamic relaxation strategies. To prove the capability and efficiency of the presented scheme, several numerical tests are performed. The results indicate that the suggested approach can trace the complex structural static paths, even in the snap-back and snap-through parts. [ABSTRACT FROM AUTHOR]

Two new shear deformable curved elements are developed for the analysis of circular and generally curved beams. The proposed scheme removes both shear and membrane lock deficiencies. In addition, effects of open radial edge cracks are included using the local flexibility approach. To form novel cracked beam finite elements, these additional flexibilities are added to those of the intact curved beam element. As a result, authors' formulation is appropriate for fracture mechanic applications, as well as the crack detection methods based on the vibration analysis. Various numerical examples evaluate the accuracy and efficiency of the proposed elements in computation of forces, displacements and frequencies of cracked and non-cracked structures. [ABSTRACT FROM AUTHOR]

By calculating the accurate solution of the governing differential equation for a non-prismatic beam–column, the exact elemental stiffness matrix will be obtained. The Euler–Bernoulli beam theory is used in the proposed formulation. This study considers the second-order effects and flexibility of the connections and supports. The effects of the ends' flexibilities are investigated by utilising the general boundary conditions of the governing differential equation. In addition, shape factors of 2 and 4 in which the cross-section moment of inertia changes by second- and fourth-order functions through the length, respectively, are studied separately. The suggested stiffness matrix is general and can be utilised in the various analyses for a non-prismatic member belonging to a plane frame with different types of connections and restraints. It should be added that the presented stiffness matrix can be used in the finite-element method. To demonstrate the abilities of the formulation, stability analyses of columns and frames with non-prismatic members are performed. Comparing the responses with the available results shows the accuracy, efficiency and capabilities of the presented matrix. [ABSTRACT FROM AUTHOR]

The capability of nonlinear analysis methods in tracing the equilibrium path depends on how to return to static status. In this paper, some residual factors existed in the iteration steps are employed. By setting the residual load parameter to zero, minimizing its factor and the residual displacement parameter, three novel constraint equations are obtained. The new formulas are proved by numerical examples. All obtained results illustrate the minimum residual load scheme's robustness in comparison with the cylindrical arc-length algorithm and other previous strategies. Moreover, the capacities of new procedures in tracing the load and displacement limit points are assessed. [ABSTRACT FROM AUTHOR]

Dynamic relaxation method (DRM) is one of the suitable numerical procedures for nonlinear structural analysis. Adding the fictitious inertia and damping forces to the static equation, and turning it to the dynamic system, are the basis of this technique. Proper selection of the DRM artificial factors leads to the better convergence rate and efficient solutions. This study aims to increase the numerical stability, and to decrease the analysis time. To fulfil this objective, the reduction rate of analysis error for consecutive iterations is minimized. Based on this formulation, a new time step is found for the viscous dynamic relaxation. After combining this novel relationship with the other DRM factors, various geometrical nonlinear structures, such as trusses, frames, and shells, are analyzed. The obtained results verify the efficiency of authors' scheme. [ABSTRACT FROM AUTHOR]

This article is concerned with the analytical solution for a curved nanobeam based on nonlocal elasticity. The structure is made of functionally graded (FG) material, and its property varies in accordance with a power law function through the thickness. To obtain the displacement function, the static differential equations for a curved FG beam are combined with the nonlocal Eringen stress equations. By using the direct method for solving the nonlocal force-strain and moment-curvature relations covering the distributed loads, the explicit expressions of nonlocal strains are achieved. The strain-displacement relations are also employed to find displacement field. Numerical examples with different types of boundary conditions are carried out in order to investigate the effects of nonlocal parameters, the nonhomogeneity index, and geometric characteristics. [ABSTRACT FROM AUTHOR]

A new family of fully explicit time integration methods is proposed, which has second-order accuracy for structures with and without damping. Using a diagonal mass matrix, the suggested scheme remains fully explicit not only for structures with a non-diagonal damping matrix, but also when the internal force vector is a nonlinear function of velocity. The present algorithm has an acceptable domain of stability, and it is self-starting. This technique introduces effectively numerical dissipation to suppress the high-frequency spurious modes, while at the same time the lower modes are not affected too much. In addition, numerical dispersion error of the scheme is considerably smaller than that of the central difference method. Solving several linear and nonlinear problems highlights the superior performance of the authors’ approach. Findings demonstrate that solution time for the suggested scheme is much less than that of the central difference technique. The related algorithm can be easily implemented into programs, which already contain the central difference method. [ABSTRACT FROM AUTHOR]

Analysis of three-dimensional frames is a complex process. Each node of these structures has six degrees of freedom, which results in a large set of governing equations. Investigators have utilized the computer power to extend the application of numerical approaches. One of these methods is named dynamic relaxation technique. This strategy explicitly solves the simultaneous system of equations. In this scheme, the static structural equilibrium equations are converted into a dynamic one by adding fictitious mass and damping. To perform nonlinear geometric analysis of 3D frames, 12 classical DR methods are exploited. Previously, the abilities of these approaches in analyzing these structures have not been compared. In each technique, time step, mass, and damping matrices are obtained based on other researchers' works. The structural behavior is assessed with and without considering the shear deformations. For both cases, the load–displacement curves are depicted. In this article, 11 different frames are analyzed. Since a few nonlinear solutions of 3D frames are available, these structures can be used as a benchmark in the future studies. Finally, the used algorithms are graded based on their required number of iterations and analysis time. Findings prove that the Qiang, Rezaiee-Pajand and Sarafrzi techniques perform more successfully in comparison to the other schemes. [ABSTRACT FROM AUTHOR]

A cracked element is formulated using the two-filed Hellinger-Reissner functional. Due to utilization of the linear elastic fracture mechanics, only geometrical nonlinearities can be considered for the cracked element. A clear step-by-step algorithm for the element state determination is also presented. The element flexibility matrix is derived in a basic coordinate system. Co-rotational approach is used to transform the element stiffness matrix and the resisting force vector from the basic system to the global one. The suggested element is applicable for static and dynamic analysis, as well as, the stress intensity factor calculation, and also inverse crack detection. Various numerical problems verify accuracy of the proposed element for linear and nonlinear structural analysis. [ABSTRACT FROM AUTHOR]

Up to now, various flat shell’s elements are created by combining plane and bending plate elements. In the case of complicated problems with coarse distorted mesh, only using efficient element leads to the accurate responses. These kinds of the elements are insensitive to the distortion. In fact, they can identify and remove the related errors. In this paper, two internal and boundary fields are deployed in a hybrid functional for formulating the proposed plane element. The method is established based on the optimum strain states. Furthermore, Trefftz functionals for independent internal and boundary fields are employed to formulate the suggested bending element. In this procedure, the optimum strain states construct the internal field, and element’s boundary field is achieved by considering the beam behavior. Finally, the high efficiency of author’s element is assessed by solving several numerical samples. [ABSTRACT FROM AUTHOR]

Statistical time-series modeling has recently emerged as a promising and applicable methodology to structural health monitoring. In this methodology, an important step is to choose robust and optimal orders of time-series models for extracting damage-sensitive features. In this study, an iterative order determination method is proposed to determine optimal orders based on residual analysis. The proposed technique consists of identifying the best time-series model, determining the maximum orders, and selecting the optimal orders that enable the model to extract uncorrelated residuals. The application of low-pass signal filters to the process of order determination is also evaluated. In a comparative study, the influence of optimal orders on damage is assessed to perceive whether features extracted from optimal models, with and without using low-pass filters, are sensitive to damage. Experimental data of a three-story laboratory frame and a large-scale bridge are applied to demonstrate the performance and capability of the proposed method. Results show that the proposed iterative method is an efficient tool for the determination of optimal orders along with the extraction of uncorrelated residuals. [ABSTRACT FROM AUTHOR]

In this paper, a new accurate predictor-corrector time integration method is proposed, which has an appropriate stability domain. The dispersion error of the suggested approach is considerably smaller than that of the central difference scheme. Moreover, the presented technique introduces effectively numerical damping, which can be used to remove the spurious highfrequency components from the numerical responses. The authors' approach has second-order accuracy for structures with and without damping. It is worth mentioning that the scheme solves the nonlinear problems without using iterative processes. The new algorithm is tested by using several linear and nonlinear numerical examples, and the outcomes are compared against the results of the central difference and explicit second-order Runge-Kutta schemes. The findings confirm the high accuracy and good performance of the suggested technique. [ABSTRACT FROM AUTHOR]

This paper is concerned with the free vibration of a gabled frame with rotational springs at intersecting joints. Each member of the frame may have different mechanical or geometrical properties. The problem at hand is to solve the gabled frame vibration problem for the natural frequencies by applying the differential transform method (DTM). Special attention is directed towards the derivation of the governing differential equations along with boundary and compatibility conditions of the problem. Some plots of mode shapes are also presented. The problem was also solved by using the finite element method to provide an independent check on the solutions. [ABSTRACT FROM AUTHOR]

An explicit time integration method is presented for the linear and nonlinear dynamic analyses of structures. Using two parameters and employing the Taylor series expansion, a family of second-order accurate methods for the solution of dynamic problems is derived. The proposed scheme includes the central difference method as a special case, while damping is shown to exert no effect on the solution accuracy. The proposed method is featured by the following facts: (i) the relative period error is almost zero for specific values of the parameters; (ii) the numerical dissipation contained can help filter out spurious high-frequency components; and (iii) the crucial lower modes are generally unaffected in the integration. Although the proposed method is conditionally stable, it has an appropriate region of stability, and is self-starting. The numerical tests indicate the improved performance of the proposed technique over the central difference method. [ABSTRACT FROM AUTHOR]

This study deals with the geometric nonlinear analysis of the plane problem based on the corotational formulation. Both analytical solutions and hybrid stress functional will be utilized in the proposed technique. A quadrilateral four-node element with drilling degrees of freedom is proposed for the finite-element analysis. The corotational method is applied for the nonlinear behavior. In this way, small strains and rigid body motions can be separated. Based on analytical solution, the hybrid stress scheme is used in the local coordinates for small strains. By using Allman's quadratic displacement, the boundary condition for this element is introduced. In this approach, added drilling degrees of freedom increase the accuracy and robustness of the element. Furthermore, the corotational formulas are written in the local and global coordinates system to derive the nonlinear relations. These equations were solved by using the arc-length algorithm. To investigate the accuracy and capability of the suggested element, several numerical tests are performed. Findings prove the advantage of the proposed element in the geometric nonlinear analysis of plane problems. [ABSTRACT FROM AUTHOR]

In this paper, various dynamic relaxation methods are investigated for geometric nonlinear analysis of bending plates. Sixteen wellknown algorithms are employed. Dynamic relaxation fictitious parameters are the mass matrix, the damping matrix and the time step. The difference between the mentioned tactics is how to implement these parameters. To compare the efficiency of these strategies, several bending plates' problems with large deflections are solved. Based on the number of iterations and analysis time, the scores of the different schemes are calculated. These scores determine the ranking of each technique. The numerical results indicate the appropriate efficiency of Underwood and Rezaiee-Pajand & Alamatian processes for the nonlinear analysis of bending plates. [ABSTRACT FROM AUTHOR]

In this paper, the free vibration analysis of a double-beam system is investigated. This structure is formed by two beams with elastic restraints at one end and free at the other end. These beams are connected by a mass-spring device. First, the related eigenvalue problem is established in the frequency domain, employing the well-known Fourier transform. Then, by utilizing eight boundary and compatibility conditions and solving two differential equations, the eigenvalues of the system are found and tabulated for different amounts of the parameters. Furthermore, some mode shapes of the mechanical system under study are plotted for various values of the springs' stiffness. In order to verify the results, some special cases are analyzed, and their outcomes are compared with the available ones. [ABSTRACT FROM AUTHOR]

A novel second-order time integration algorithm for solving dynamic problems is presented. To demonstrate the abilities of this formulation, several linear and geometrical nonlinear structures are solved. The outcomes of authors' technique are compared with the ones obtained by other researchers. The findings not only confirm the improved accuracy of the new scheme but also indicate that the suggested method remains stable when the trapezoidal rule fails to produce a stable solution. Effectively maximizing high-frequency numerical dissipation, without inducing excessive algorithmic damping in the important low-frequency region, is one of the proposed tactic merits. Spurious oscillations are removed, and small numerical dispersion error is achieved, when using this approach. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to introduce an efficient procedure for crack detection in concrete gravity dams. A genetic algorithm and finite-element modelling are employed to perform the optimisation tasks. A two-dimensional cracked element is formulated for non-linear analysis. In this investigation, the kinematics of the discontinuous displacement field in a body with an internal discontinuity is utilised. Based on the suggested interpolation functions for the discrete segments, and also the element displacement field, the element stiffness matrix is calculated. Moreover, a genetic algorithm approach for crack identification is proposed, which can identify the location and magnitude of cracks in concrete gravity dams. By minimising the difference between the analytical responses given by the authors' element and the measured ones, the genetic algorithm identifies the crack. Finally, several numerical examples are analysed for the accuracy test and a few of them are presented here. [ABSTRACT FROM AUTHOR]

Many triangular elements have been formulated for bending plate analysis so far. In this type of element, researchers generally considered the same distance between the side nodes. The present study will show that these types of node locations are not the best. To clarify the effect of side node locations, three new triangular elements will be formulated for the analysis of thin bending plates. These are nonconforming elements and have 10, 15, and 21 degrees of freedom, respectively. Merits and disadvantages of these proposed elements will be revealed by solving different structures. Optimal side nodes' location will be positioned by changing the place of element nodes. Numerical tests will confirm that element accuracy in the best possible situation is much better than the state in which side nodes have the same distance. Moreover, this study will reveal that the presented optimal locations of nodes have no significant dependence on the load cases, boundary conditions, distortion of element shape, and variation of the meshes [ABSTRACT FROM AUTHOR]

In the present study, two semi-implicit schemes, based on the exponential maps method, are derived for integrating the pressure-sensitive constitutive equations. In spite of the fact that the consistent tangent operator is necessary to preserve the quadratic rate for the asymptotic convergence of the Newton-Raphson solution in the finite element analyses, there exists no derivation of this operator for the exponential-based integrations of the pressure-sensitive plasticity in the literature. To fulfill this need, the algorithmic tangent operators are extracted for the new semi-implicit as well as the former exponential-based integrations. Moreover, for the accurate integration presented by Rezaiee-Pajand et al. (Eur J Mech A Solids 30:345-361, ), the consistent tangent operator is obtained. Eventually, all the investigations are assessed by a broad range of numerical tests. [ABSTRACT FROM AUTHOR]

In this paper, two efficient elements are proposed by utilizing hybrid Trefftz method for the analysis of thin plate bending. The triangular element, THT, and the quadrilateral element, QHT, which have 9 and 12 degrees of freedom, respectively. Two independent displacement fields are defined for internal and boundary of the elements. The internal field is selected in such a way that it satisfies the governing equation of the thin plate. Boundary field is dependent on the nodal degrees of freedom via boundary interpolation functions. For deriving boundary interpolation functions, element's edges are assumed to deform like a beam, and the related interpolation functions are used for the boundary fields. The solution accuracies of the famous and hard bench mark problems, such as circular and skew plates, prove the justification of suggested elements. Based on the various test problems, QHT in comparison to other four-sided elements, and THT in comparison to triangular ones, show better results and rapider convergence rate. [ABSTRACT FROM AUTHOR]

The stability and accuracy of two families of time integration algorithms are investigated in this study. The paper has three intended goals. The first one is to find the precise properties of the implicit higher-order accuracy methods. The capabilities of the family members are found both by analytical and numerical procedures. The second goal is to find the well-defined characteristics of the predictor-corrector methods. For application purposes, the best order of each family is introduced by this investigation. Numerical results show that the stability properties of the implicit high-order accuracy and predictor-corrector methods are approximately the same. As a third goal, a modified dynamic relaxation method is also developed for non-linear dynamic analyses. This is a robust scheme that uses less memory and requires less computational effort, in comparison with the previous version of dynamic relaxation method. [ABSTRACT FROM AUTHOR]