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21 – 30 of over 8000Kaveh Salmalian, Ali Alijani and Habib Ramezannejad Azarboni
The purpose of this study is to investigate the post-buckling analysis of functionally graded columns by using three analytical, approximate and numerical methods. A pre-defined…
Abstract
Purpose
The purpose of this study is to investigate the post-buckling analysis of functionally graded columns by using three analytical, approximate and numerical methods. A pre-defined function as an initial assumption for the post-buckling path is introduced to solve the differential equation. The finite difference method is used to approximate the lateral deflection of the column based on the differential equation. Moreover, the finite element method is used to derive the tangent stiffness matrix of the column.
Design/methodology/approach
The non-linear buckling analysis of functionally graded materials is carried out by using three analytical, finite difference and finite element methods. The elastic deformation and Euler-Bernoulli beam theory are considered to establish the constitutive and kinematics relations, respectively. The governing differential equation of the post-buckling problem is derived through the energy method and the calculus variation.
Findings
An incremental iterative solution and the perturbation of the displacement vector at the critical buckling point are performed to determine the post-buckling path. The convergence of the finite element results and the effects of geometric and material characteristics on the post-buckling path are investigated.
Originality/value
The key point of the research is to compare three methods and to detect error sources by considering the derivation process of relations. This comparison shows that a non-incremental solution in the analytical and finite difference methods and an initial assumption in the analytical method lead to an error in results. However, the post-buckling path in the finite element method is traced by the updated tangent stiffness matrix in each load step without any initial limitation.
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J. Sorić, U. Montag and W.B. Krätzig
Presents a robust and unconditionally stable return‐mapping algorithm based on the discrete counterpart of the principle of maximum plastic dissipation. Develops the explicit…
Abstract
Presents a robust and unconditionally stable return‐mapping algorithm based on the discrete counterpart of the principle of maximum plastic dissipation. Develops the explicit expression for the consistent elasto‐plastic tangent modulus. All expressions are derived via tensor formulation showing the advantage over the classical matrix notation. The integration algorithm is implemented in the formulation of the four‐node isoparametric assumed‐strain finite‐rotation shell element employing the Mindlin‐Reissner‐type shell model. By applying the layered model, plastic zones can be displayed through the shell thickness. Material non‐linearity described by the von Mises yield criterion and isotropic hardening is combined with a geometrically non‐linear response assuming finite rotations. Numerical examples illustrate the efficiency of the present formulation in conjunction with the standard Newton iteration approach, in which no line search procedures are required. Demonstrates the excellent performance of the algorithm for large time respective load steps.
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Dominique Lochegnies and Jerome Oudin
New contact boundary modelling is achieved with a basic set of 2 and 3dimension contact primitives. Contact constraints are originally introducedin the variational equations and…
Abstract
New contact boundary modelling is achieved with a basic set of 2 and 3 dimension contact primitives. Contact constraints are originally introduced in the variational equations and associated Newton—Raphson scheme via an external penalty formulation using primitive equations. Consequently, penalty part of external load vector and tangent stiffness matrices are developed for all contact primitives. In this way, contact prescribed boundary displacements are also taken into account. Contact treatment is then completed with Newton—Raphson elements for elastic and plastic regularized friction constitutive models. In this paper, the process is extended to elastoplastic models. Finally, we propose a self acting procedure with contact algorithms (interiority, sliding and contact loss) and related subroutines for implementation in finite element framework. We illustrate these developments by means of two‐dimensional open die forging and three‐dimensional plate coining typical benchmarks with reference to bulk elastoplastic and viscoplastic constitutive models.
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The simplest facet‐shell formulation involves the combination of the constant‐strain membrane triangle with a constant‐curvature bending triangle. The paper first describes an…
Abstract
The simplest facet‐shell formulation involves the combination of the constant‐strain membrane triangle with a constant‐curvature bending triangle. The paper first describes an alternative co‐rotational procedure to the one initially proposed by Peng and Crisfield in 1992. This new formulation introduces a spin matrix which allows a simpler formulation for the consistent tangent stiffness matrix. The paper then moves to the dynamics of the element. To obtain stable solutions, an energy‐conserving mid‐point time‐integration scheme is developed. This scheme exactly conserves the total energy when external forces are constant and when the physical system does not present any damping. The performance of this scheme is compared with other more conventional implicit schemes through a set of numerical examples involving large‐scale rotations.
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Many engineering structures exhibit loss of stability under static and dynamic loading. Due to the significance of these phenomena in engineering design this topic has attracted…
Abstract
Many engineering structures exhibit loss of stability under static and dynamic loading. Due to the significance of these phenomena in engineering design this topic has attracted considerable attention during the last decades. In recent years much effort has been made to devise algorithms within finite element analysis to investigate the static stability behaviour of structures. With these methods stable and unstable paths can be traced, and limit or bifurcation points can be computed efficiently. The associated arc‐length or branch‐switching procedures are today standard tools in existing finite element codes.
E. Oñate, H. Tschöpe and P. Wriggers
The paper describes the extension of the critical displacement method (CDM), presented by Oñate and Matias in 1996, to the instability analysis of structures with non‐linear…
Abstract
The paper describes the extension of the critical displacement method (CDM), presented by Oñate and Matias in 1996, to the instability analysis of structures with non‐linear material behaviour using a simple damage model. The extended CDM is useful to detect instability points using a prediction of the critical displacement field and a secant load‐displacement relationship accounting for material non‐linearities. Examples of application of CDM to the instability analysis of structures using bar and solid finite elements are presented.
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The purpose of this paper is to expand the previously published fuzzy logic controller for contact method to normal frictionless contact for solving mechanical frictional contact…
Abstract
Purpose
The purpose of this paper is to expand the previously published fuzzy logic controller for contact method to normal frictionless contact for solving mechanical frictional contact problems. The secondary aim is to integrate a reduction model for each component in contact to decrease the size of the global finite element contact problem.
Design/methodology/approach
The proposed strategy relies on the design of two fuzzy logic controllers currently used in the automation domain. These controllers are considered to link normal and tangential gaps (for sticking conditions) with normal and tangential contact loads. A direct consequence of integrating a control-based approach into the numerical solving approach is the decomposition of the non-linear problem into a set of linear problems.
Findings
With this new strategy, no tangent or coupling matrix is defined for the contact problem that allows to consider a projection matrix to reduce the size of each component in contact and subsequently to decrease the associated computational time. As in condensation techniques, this matrix is composed of both modal bases of each component in contact and static modes that capture behaviors at the contact interface. Moreover, the proposed numerical application highlights the efficiency of the proposal in terms of computation time and precision of contact data.
Research limitations/implications
The developments are currently implemented in Matlab only for 2D static numerical applications. Therefore, as obtained results are very promising in terms of precision and computational time, the objective is to complete the proposed method in future research to manage frictional contact for 3D finite element models in a dynamic context.
Originality/value
In conclusion, this paper highlights the interest of studying mechanical frictional contact problems by considering fuzzy logic control approaches.
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A stiffened shell element is presented for geometricallynon‐linear analysis of eccentrically stiffened shell structures.Modelling with this element is more accurate than with the…
Abstract
A stiffened shell element is presented for geometrically non‐linear analysis of eccentrically stiffened shell structures. Modelling with this element is more accurate than with the traditional equivalent orthotropic plate element or with lumping stiffeners. In addition, mesh generation is easier than with the conventional finite element approach where the shell and beam elements are combined explicitly to represent stiffened structures. In the present non‐linear finite element procedure, the tangent stiffness matrix is derived using the updated Lagrangian formulation and the element strains, stresses, and internal force vectors are updated employing a corotational approach. The non‐vectorial characteristic of large rotations is taken into account. This stiffened shell element formulation is ideally suited for implementation into existing linear finite element programs and its accuracy and effectiveness have been demonstrated in several numerical examples.
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Ani Luo, Ziying Cao, Heping Liu and Yaming Feng
In this paper, the main factors influencing the structure stiffness will be analyzed by studying the tangent stiffness matrix based on different requirement in engineering…
Abstract
Purpose
In this paper, the main factors influencing the structure stiffness will be analyzed by studying the tangent stiffness matrix based on different requirement in engineering practice. The authors can obtain the deformation of three-bar tensegrity basic unit in different load, and gain the primary factor by comparing the deformation, which will provide reference to concrete structure design in the engineering.
Design/methodology/approach
The mathematical model of tensegrity structure was built by establishing generalized node coordinates and connective matrix. Three main factors that affect the structure deformation can be obtained by analyzing the stiffness matrix, which is preload, Young's modulus, and cross-sectional area, the thinking of deformation also be sorted out. The deformation analysis of the concrete structure is carried out, and it is concluded that increasing the cross-sectional area can quickly improve the stiffness of the structure, which provides a reference for the structural variable stiffness design in practical engineering.
Findings
(1) When the axial external force is applied to the structure, the torsion-angle deformation of the structure is the largest, and the radial deformation of the structure is the smallest. (2) The structure stiffness can be rapidly enhanced by increasing the cross-sectional area. But the cross-sectional area can't be increased indefinitely. Because the mass will be increased once increasing the cross-sectional area, which will destroy the structure of the advantages of light weight in engineering practice.
Originality/value
The deformation analysis of the concrete structure is carried out, and it is concluded that increasing the cross-sectional area can quickly improve the stiffness of the structure, which provides a reference for the structural variable stiffness design in practical engineering.
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Mohammad Rezaiee‐Pajand, Cyrus Nasirai and Mehrzad Sharifian
The purpose of this paper is to present a new effective integration method for cyclic plasticity models.
Abstract
Purpose
The purpose of this paper is to present a new effective integration method for cyclic plasticity models.
Design/methodology/approach
By defining an integrating factor and an augmented stress vector, the system of differential equations of the constitutive model is converted into a nonlinear dynamical system, which could be solved by an exponential map algorithm.
Findings
The numerical tests show the robustness and high efficiency of the proposed integration scheme.
Research limitations/implications
The von‐Mises yield criterion in the regime of small deformation is assumed. In addition, the model obeys a general nonlinear kinematic hardening and an exponential isotropic hardening.
Practical implications
Integrating the constitutive equations in order to update the material state is one of the most important steps in a nonlinear finite element analysis. The accuracy of the integration method could directly influence the result of the elastoplastic analyses.
Originality/value
The paper deals with integrating the constitutive equations in a nonlinear finite element analysis. This subject could be interesting for the academy as well as industry. The proposed exponential‐based integration method is more efficient than the classical strategies.
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