• Structural Engineering and Mechanics
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• v.17 no.6
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• pp.829-862
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• 2004

This paper presents a method for the nonlinear analysis of beam elements subjected to the cyclical combined actions of torsion, biaxial flexure and axial forces based on an extension of the disturbed compression field (DSFM). The theoretical model is based on a hybrid formulation between the full rotation of the cracks model and the fixed direction of the cracking model. The described formulation, which treats cracked concrete as an orthotropic material, includes a new approach for the evaluation of the re-orientation of both the compression field and the deformation field by removing the restriction of their coincidence. A new equation of congruence permits evaluating the deformation of the middle line. The problem consists in the solution of coupled nonlinear simultaneous equations expressing equilibrium, congruence and the constitutive laws. The proposed method makes it possible to determine the deformations of the beam element according to the external stresses applied.

• Advances in aircraft and spacecraft science
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• v.3 no.3
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• pp.317-330
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• 2016

Nowadays, the interest of aerospace and automotive industries on virtual testing of medium-frequency vibrational behavior of shallow shell structures is growing. The development of software capable of predicting the vibrational response in such frequency range is still an open question because classical methods (i.e., FEM, SEA) are not fully suitable for the medium-frequency bandwidth. In this context the Variational Theory of Complex Rays (VTCR) is taking place as an ad-hoc technique to address medium-frequency problems. It is a Trefftz method based on a weak variational formulation. It allows great flexibility because any shape function that satisfies the governing equations can be used. This work further develops such theory. In particular, orthotropic materials are introduced in the VTCR formulation for shallow shell structures. A significant numerical example is proposed to show the strategy.

• Structural Engineering and Mechanics
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• v.35 no.3
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• pp.315-333
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• 2010

The structural behaviors of circular concrete filled steel tube (CFT) structures are investigated by nonlinear finite element method. An efficient three-dimensional (3D) degenerated beam element is adopted. Based on those previous studies, a modified stress-strain relationship for confined concrete which introduces the influence of eccentricity on confining stress is presented. Updated Lagrange formulation is used to consider the geometrical nonlinearity induced by large deformation effect. The nonlinear behaviors of CFT structures are investigated, and the accuracy of the proposed constitutive model for confined concrete is mainly concerned. The results demonstrate that the confining effect in CFT elements subjected to combining action of axial force and bending moment is far sophisticated than that in axial loaded columns, and an appropriate evaluation about this effect may be important for nonlinear numerical simulation of CFT structures.

• Journal of Hydrospace Technology
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• v.1 no.1
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• pp.14-28
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• 1995

The hydrodynamic problem when the pressurized bag submerges partially into water and oscillates was formulated by Lee(1992), and the solution method was given, In his formulation, however, the compressilbility of air was neglected and the pressure inside the bag was assumed to be constant. In this paper, the formulation was done including the air compressibility and the wall to block fling around phenomenon. The compression process was assumed to be a isothermal process for a static problem, isentropic process for a dynamic problem. And the stability was analyzed for the static problem. Through the various numerical calculations, the forces and the shape of the bag were compared with those of a rigid body case, constant pressure case, and variable pressure case.

• Earthquakes and Structures
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• v.17 no.1
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• pp.101-113
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• 2019

Earthquake-induced pounding is one of the major reasons for structural failure in earthquake prone cities. An accurate description of the pounding phenomenon of two buildings requires the consideration of systems with a large number of degrees of freedom including adequate contact impact formulations. In this paper, firstly, a node to surface formulation for the realization of state-of-the-art pounding models for structural beam elements is presented. Secondly, a hierarchical substructure technique is introduced, which is adapted to the structural pounding problem. The numerical accuracy and efficiency of the method, especially for the contact forces, are verified on an academic example, applying four different impact elements. Error estimations are carried out and compared with the classical modal truncation method. It is demonstrated that the hierarchical substructure method is indeed able to significantly speed up the numeric integration procedure by preserving a required level of accuracy.

• Structural Engineering and Mechanics
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• v.69 no.4
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• pp.427-437
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• 2019

In this study, an alternative solution procedure presented by using variational methods for analysis of shear deformable functionally graded material (FGM) beams with mixed formulation. By using the advantages of $G{\hat{a}}teaux$ differential approaches, a refined complex general functional and boundary conditions which comprises seven independent variables such as displacement, rotation, bending moment and higher-order bending moment, shear force and higher-order shear force, is derived for general thick-thin FGM beams via shear deformation beam theories. The mixed-finite element method (FEM) is employed to obtain a beam element which have a 2-nodes and total fourteen degrees-of-freedoms. A computer program is written to execute the analyses for the present study. The numerical results of analyses obtained for different boundary conditions are presented and compared with results available in the literature.

• Structural Engineering and Mechanics
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• v.68 no.6
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• pp.639-646
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• 2018

The aim of the present paper deals with free vibration analysis of laminated composite skew plates with single and multiple cut-outs. For complete understanding of the dynamic behavior of laminated skew plates with cut-out a numerical analysis has been carried out by developing a computer code in FOTRAN. Special attention is drawn on the formulation of mass matrix by considering effect of rotary inertia. The results obtained by the finite element formulation using nine noded isoparametric plate bending element are validated by comparing the results from relevant published literature. Few new results on laminated skew plates with cut-out have been presented.

• Advances in nano research
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• v.15 no.2
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• pp.141-153
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• 2023

The main objective of this paper is to develop the finite element study on the nonlinear free vibration of functionally graded nanocomposite spherical shells reinforced with graphene platelets under the first-order shear deformation shell theory and von Kármán nonlinear kinematic relations. The governing equations are presented by introducing the full asymmetric nonlinear strain-displacement relations followed by the constitutive relations and energy functional. The extended Halpin-Tsai model is utilized to specify the overall Young's modulus of the nanocomposite. Then, the finite element formulation is derived and the quadrilateral 8-node shell element is implemented for finite element discretization. The nonlinear sets of dynamic equations are solved by the use of the harmonic balance technique and iterative method to find the nonlinear frequency response. Several numerical examples are represented to highlight the impact of involved factors on the large-amplitude vibration responses of nanocomposite spherical shells. One of the main findings is that for some geometrical and material parameters, the fundamental vibrational mode shape is asymmetric and the axisymmetric formulation cannot be appropriately employed to model the nonlinear dynamic behavior of nanocomposite spherical shells.

• Structural Engineering and Mechanics
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• v.87 no.4
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• pp.363-373
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• 2023

Since the first family of structure-dependent methods can simultaneously integrate unconditional stability and explicit formulation in addition to second order accuracy, it is very computationally efficient for solving inertial problems except for adopting auto time-stepping techniques due to no nonlinear iterations. However, an unusual stability property is first found herein since its unconditional stability interval is drastically different for zero and nonzero damping. In fact, instability might occur for solving a damped stiffness hardening system while an accurate result can be obtained for the corresponding undamped stiffness hardening system. A technique of using a stability factor is applied to overcome this difficulty. It can be applied to magnify an unconditional stability interval. After introducing this stability factor, the formulation of this family of structure-dependent methods is changed accordingly and thus its numerical properties must be re-evaluated. In summary, a large stability factor can result in a large unconditional stability interval but also lead to a large relative period error. As a consequence, a stability factor must be appropriately chosen to have a desired unconditional stability interval in addition to an acceptable period distortion.

• Steel and Composite Structures
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• v.45 no.4
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• pp.535-546
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• 2022

The memory response of nonlocal systematical formulation size-dependent coupling of viscoelastic deformation and thermal fields for piezoelectric materials with dual-phase lag heat conduction law is constructed. The method of the matrix exponential, which constitutes the basis of the state-space approach of modern control theory, is applied to the non-dimensional equations. The resulting formulation together with the Laplace transform technique is applied to solve a problem of a semi-infinite piezoelectric rod subjected to a continuous heat flux with constant time rates. The inversion of the Laplace transforms is carried out using a numerical approach. Some comparisons of the impacts of nonlocal parameters and time-delay constants for various forms of kernel functions on thermal spreads and thermo-viscoelastic response are illustrated graphically.