• Structural Engineering and Mechanics
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• v.8 no.6
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• pp.607-622
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• 1999

Being a significant mode of deformation, shear effect in addition to the other modes of stretching and bending have been considered to develop two finite element models for the analysis of beams on elastic foundation. The first beam model is developed utilizing the differential-equation approach; in which the complex variables obtained from the solution of the differential equations are used as interpolation functions for the displacement field in this beam element. A single element is sufficient to exactly represent a continuous part of a beam on Winkler foundation for cases involving end-loadings, thus providing a benchmark solution to validate the other model developed. The second beam model is developed utilizing the hybrid-mixed formulation, i.e., Hellinger-Reissner variational principle; in which both displacement and stress fields for the beam as well as the foundation are approxmated separately in order to eliminate the well-known phenomenon of shear locking, as well as the newly-identified problem of "foundation-locking" that can arise in cases involving foundations with extreme rigidities. This latter model is versatile and indented for utilization in general applications; i.e., for thin-thick beams, general loadings, and a wide variation of the underlying foundation rigidity with respect to beam stiffness. A set of numerical examples are given to demonstrate and assess the performance of the developed beam models in practical applications involving shear deformation effect.

• Interaction and multiscale mechanics
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• v.6 no.2
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• pp.173-195
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• 2013

Meshfree methods are known to have the capability to overcome the strict regularization requirements and numerical instabilities that encumber the finite element method (FEM) in large deformation problems. They are also more naturally suited for problems involving material perforation and fragmentation. To take advantage of the high efficiency of FEM and high accuracy of meshfree methods, a coupled finite element (FE) and reproducing kernel (RK, one of the meshfree approximations) formulation is described in this paper. The coupling of FE and RK approximation is implemented in an evolutionary fashion, where the extent and location of the evolution is dependent on a triggering criteria provided by the material constitutive laws. To enhance computational efficiency, Gauss quadrature is applied to integrate both FE and RK domains so that no state variable transfer is required when mesh conversion is performed. To control the hourglassing that might occur with 1-point integrated hexahedral grids, viscous type hourglass control is implemented. Meanwhile, the FEM version of the K&C concrete (KCC) model was modified to make it applicable in both FE and RK formulations. Results using this code and the KCC model are shown for the modeling of concrete responses under quasi-static, blast and impact loadings. These analyses demonstrate that fragmentation phenomena of the sort commonly observed under blast and impact loadings of concrete structures was able to be realistically captured by the coupled formulation.

• Smart Structures and Systems
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• v.25 no.6
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• pp.693-705
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• 2020

In the current investigation, large amplitude free vibration behavior of shallow curved pipes (tubes) made of functionally graded materials is investigated. Properties of the tube are distributed across the radius of the tube and are obtained by means of a power law function. It is also assumed that all thermo-mechanical properties are temperature dependent. The governing equations of the tube are obtained using a higher order shear deformation tube theory, where the traction free boundary conditions are satisfied on the top and bottom surfaces of the tube. The von Kármán type of geometrical non-linearity is included into the formulation to consider the large displacements and small strains. Uniform temperature elevation of the tube is also included into the formulation. For the case of tubes which are simply supported in flexure and axially immovable, the governing equations are solved using the two-step perturbation technique. Closed form expressions are provided to obtain the small and large amplitude fundamental natural frequencies of the FGM shallow curved tubes in thermal environment. Numerical results are given to explore the effects of thermal environment, radius ratio, and length to thickness ratio of the tube on the fundamental linear and non-linear frequencies.

• Structural Engineering and Mechanics
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• v.74 no.2
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• pp.297-311
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• 2020

The main purpose of this study is to analyze the effects of external pressure on the vibration and buckling of functionally graded (FG) spherical panels resting of elastic medium. The material characteristics of the FG sphere continuously vary through the thickness direction based on the power-law rule. In accordance with first-order shear deformation shell theory and by the use of Ritz formulation the governing equations are presented. In this regard, the beam functions are applied in two-dimensions for different sets of boundary supports. The Winkler and Pasternak models of elastic foundations are also taken into account. In order to show the validity and applicability of the presented formulation, various comparison studies are given. Furthermore, a diverse range of numerical results is reported to check the impacts of geometrical and material parameters along with external pressure on the vibration and buckling analysis of FG spherical panels.

• International Journal of Aerospace System Engineering
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• v.2 no.2
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• pp.19-23
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• 2015

This work deals with the study of buckling and post buckling characteristics of laminated composite plates with and without localized regions of damage. The need of a detailed study on Finite Element Analysis of buckling and post buckling of laminated composite structures considering various aspects enhances the interest among researchers. Mathematical formulation is developed for damaged composite plates using a finite element technique based on Inverse Hyperbolic Shear Deformation Theory. This theory satisfies zero transverse shear stresses conditions at the top and bottom surfaces of the plate and provides a non-linear transverse shear stress distribution. Damage modeling is done using an anisotropic damage formulation, which is based on the concept of stiffness change. The structural elements are subjected to in-plane loading. The computer program is developed in MATLAB environment. The numerical results are presented after through validation of developed finite element code. The effect of damage on buckling and post buckling has been carried out for various parameters such as amount of percentage of damaged area, damage intensity, etc. The results show that the presence of internal flaws will significantly affect the buckling characteristics of laminated composite plates. The outcomes and remarks from this work will assist to address some key issues concerning composite structures.

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.7
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• pp.559-567
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• 2000

This paper proposes simple and practical methods in order to overcome complex formulation and heavy computational burden of the forward kinematics of 6 앨 3-6 type parallel manipulators. Three ap-proaches for the forward kinematics are presented : one extra sensor a modified structure and novel numerical method. The proposed methods are applied to the forward kinematics of a new 6 앨 parallel manipulator with special geometry that has three internal links three external links and a moving platform of a cone shape. The proposed methods use three tetrahedrons for finding the position and orientation vector of the moving platform. The main advantages of the appraches using tetrahedrons are to abbreviate the formulation to easily find so-lutions of the forward kinematics and to be able to practically control of the manipulator in real time.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.319-326
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• 2002

A p-version finite element model based on degenerate shell element is proposed for the analysis of orthotropic laminated plates. In the nonlinear formulation of the model, the total Lagrangian formulation is adopted with large deflection and moderate rotation being accounted for in the sense of von Karman hypothesis. The material model Is based on the Huber-Mises yield criterion and Prandtl-Reuss flow rule in accordance with the theory of strain hardening yield function, which is generalized for anisotropic materials by introducing the parameters of anisotropy. The model is also based on extension of equivalent-single layer laminate theory(ESL theory) with shear deformation, leading to continuous shear strain at the interface of two layers. The Integrals of Legendre Polynomials we used for shape functions with p-level varying from 1 to 10. Gauss-Lobatto numerical quadrature is used to calculate the stresses at the nodal points instead of Gauss points. The validity of the proposed p-version finite element model is demonstrated through several comparative points of view in terms of ultimate load, convergence characteristics, nonlinear effect, and shape of plastic zone

• Structural Engineering and Mechanics
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• v.51 no.5
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• pp.847-866
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• 2014

This paper describes a formulation to predict optimum post-tensioning forces and cable dimensioning for self-anchored cable-stayed suspension bridges. The analysis is developed with respect to both dead and live load configurations, taking into account design constrains concerning serviceability and ultimate limit states. In particular, under dead loads, the analysis is developed with the purpose to calculate the post-tensioning cable forces to achieve minimum deflections for both girder and pylons. Moreover, under live loads, for each cable elements, the lowest required cross-section area is determined, which verifies prescriptions, under ultimate or serviceability limit states, on maximum allowable stresses and bridge deflections. The final configuration is obtained by means of an iterative procedure, which leads to a progressive definition of the stay, hanger and main cable characteristics, concerning both post-tensioning cable stresses and cross-sections. The design procedure is developed in the framework of a FE modeling, by using a refined formulation of the bridge components, taking into account of geometric nonlinearities involved in the bridge components. The results demonstrate that the proposed method can be easily utilized to predict the cable dimensioning also in the framework of long span bridge structures, in which typically more complexities are expected in view of the large number of variables involved in the design analysis.

• Steel and Composite Structures
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• v.6 no.3
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• pp.237-255
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• 2006

This paper presents a novel analytical formulation for the analysis of composite beams with partial shear interaction stiffened by a bolted longitudinal plate accounting for time effects, such as creep and shrinkage. The model is derived by means of the principle of virtual work using a displacement-based formulation. The particularity of this approach is that the partial interaction behaviour is assumed to exist between the top slab and the joist as well as between the joist and the bolted longitudinal stiffening plate, therefore leading to a three-layered structural representation. For this purpose, a novel finite element is derived and presented. Its accuracy is validated based on short-and long-term analyses for the particular cases of full shear interaction and partial shear interaction of two layers for which solutions in closed form are available in the literature. A parametric study is carried out considering different stiffening arrangements to investigate the influence on the short-and long-term behaviour of the composite beam of the shear connection stiffness between the concrete slab and the steel joist, the stiffness of the plate-to-beam connection, the properties of the longitudinal plate and the concrete properties. The values of the deflection obtained from the finite element simulations are compared against those calculated using the effective flexural rigidity in accordance with EC5 guidelines for the behaviour of elastic multi-layered beams with flexible connection and it is shown how the latter well predicts the structural response. The proposed numerical examples highlight the ease of use of the proposed approach in determining the effectiveness of different retrofitting solutions at service conditions.

• Computers and Concrete
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• v.8 no.4
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• pp.371-388
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• 2011

In this paper, time-continuous constitutive equations for strain rate-dependent materials are presented first, among which those for the overstress and the consistency viscoplastic models are considered. By allowing the stress states to be outside the yield surface, the overstress viscoplastic model directly defines the flow rule for viscoplastic strain rate. In comparison, a rate-dependent yield surface is defined in the consistency viscoplastic model, so that the standard Kuhn-Tucker loading/unloading condition still remains true for rate-dependent plasticity. Based on the formulation of the consistency viscoplasticity, a computational elasto-viscoplastic constitutive model is proposed for the short fiber-reinforced fresh cementitious paste for extrusion purpose. The proposed constitutive model adopts the von-Mises yield criterion, the associated flow rule and nonlinear strain rate-hardening law. It is found that the predicted flow stresses of the extrudable fresh cementitious paste agree well with experimental results. The rate-form constitutive equations are then integrated into an incremental formulation, which is implemented into a numerical framework based on ANSYS/LS-DYNA finite element code. Then, a series of upsetting and ram extrusion processes are simulated. It is found that the predicted forming load-time data are in good agreement with experimental results, suggesting that the proposed constitutive model could describe the elasto-viscoplastic behavior of the short fiber-reinforced extrudable fresh cementitious paste.