scholarly journals Beam element for large displacement analysis of elasto-plastic frames

2004 ◽  
Vol 26 (1) ◽  
pp. 39-54
Author(s):  
Nguyen Dinh Kien ◽  
Do Quoc Quang
Keyword(s):  
Virtual Work ◽  
Internal Force ◽  
Beam Element ◽  
Large Displacement ◽  
Isotropic Hardening ◽  
Arc Length ◽  
Tangent Stiffness Matrix ◽  
Strain Relationship ◽  
Internal Force Vector ◽  
Finite Element Formulations

The present paper develops a non-linear beam element for analysis of elastoplastic frames under large displacements. The finite element formulations are derived by using the co-rotational approach and expression of the virtual work. The Gauss quadrature is employed for numerically computing the element tangent stiffness matrix and internal force vector. A bilinear stress-strain relationship with isotropic hardening is adopted to update the stress. The arc-length technique based on the Newton-Raphson iterative method is employed to compute the equilibrium paths. A number of numerical examples is employed to assess the performance of the developed element. The effects of plastic action on the large displacement behavior of the structures as well as the expansion of plastic zones in the loading process are discussed.

scholarly journals Effects of shear deformation on large deflection behavior of elastic frames

2004 ◽  
Vol 26 (3) ◽  
pp. 167-181
Author(s):  
Nguyen Dinh Kien
Keyword(s):  
Shear Deformation ◽  
Stiffness Matrix ◽  
Large Deflection ◽  
Beam Element ◽  
Control Technique ◽  
Arc Length ◽  
The Finite Element Method ◽  
Nonlinear Beam ◽  
Tangent Stiffness Matrix ◽  
Lowest Eigenvalue

In this paper, the effects of shear deformation on the large deflection behavior of elastic frames is investigated by the finite element method. A two-node nonlinear beam element with the shear deformation is formulated and employed to analyze some frame structures. The element based on the energy method is developed in the context of the corotational approach. A bracketing procedure u ed the lowest eigenvalue of structural tangent stiffness matrix as indicating parameter is adopted to compute the critical loads. An incremental iterative procedure with the arc-length control technique is employed to trace the equilibrium paths. The numerical results show that the shear deformation plays an important role in the critical load and the large deflection behavior of the frames constructed from the components having low slenderness. A detail investigation is carried out to highlight the influence of slenderness on the behavior of the frames under large deflection.

scholarly journals Uma abordagem analítica para detecção de pontos limites e de bifurcação

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
William Taylor Matias Silva ◽  
Maria Paz Duque Gutierrez ◽  
Wellington Andrade Da Silva
Keyword(s):  
Axial Stress ◽  
Strain Tensor ◽  
Uniaxial Stress ◽  
Internal Force ◽  
Structural Systems ◽  
Equilibrium Path ◽  
Tangent Stiffness Matrix ◽  
Physical Conditions ◽  
Internal Force Vector ◽  
Lagrange Strain

RESUMO: Neste trabalho descreve-se analiticamente de maneira detalhada a detecção e a classificação de pontos críticos na trajetória primária de equilíbrio de sistemas estruturais. Utiliza-se a Formulação Lagrangiana Total para descrever a cinemática de um elemento de barra biarticulado 2D. Através desta formulação obtém-se o vetor de forças internas e a matriz de rigidez tangente que levam em conta os efeitos da não linearidade geométrica. Assume-se um modelo constitutivo linear elástico para o estado uniaxial de tensão-deformação, usando a deformação de Green-Lagrange e a tensão axial do segundo tensor de Piola-Kirchhoff que são energeticamente conjugados. Como estudo de caso apresenta-se uma treliça plana hiperestática composta com 3 elementos biarticulados 2D e com dois graus de liberdade. Por fim, determinam-se as condições geométricas e físicas para a coalescência entre os pontos limites e de bifurcação. A principal contribuição deste trabalho é demonstrar a necessidade de compreender melhor os fenômenos não lineares para projetar sistemas estruturais mais seguros. ABSTRACT: Using an analytical this paper describes in detail the detection and classification of critical points in the primary equilibrium path of structural systems. The Total Lagrangian formulation is employed to describe the kinematics of a 2D bar element. With this formulation, the internal force vector and the tangent stiffness matrix including the geometric nonlinearity effects are obtained. An elastic linear constitutive model is assumed for the uniaxial stress-strain state. Such model uses the Green-Lagrange strain tensor and the second Piola-Kirchhoff axial stress tensor which are energetically conjugate tensors. As a study case, the article presents a statically inderminate plane truss discretized with three 2D bar elements. Finally, the geometrical and physical conditions for the coalescence between limit and bifurcation points are determined. The main contribution of this work is to demonstrate the need to better understanding the non linear phenomena. Such understanding is necessary for designing safer structural systems.

LARGE DISPLACEMENT BEAM MODEL FOR CREEP BUCKLING ANALYSIS OF FRAMED STRUCTURES

2009 ◽  
Vol 09 (01) ◽  
pp. 61-83 ◽  
Author(s):  
GORAN TURKALJ ◽  
DOMAGOJ LANC ◽  
JOSIP BRNIC
Keyword(s):  
Virtual Work ◽  
Buckling Analysis ◽  
Large Displacement ◽  
Isotropic Hardening ◽  
Beam Model ◽  
Inelastic Behavior ◽  
Equilibrium Equations ◽  
Virtual Work Principle ◽  
Framed Structures ◽  
Spatial Beam

In this work, a one-dimensional beam model for buckling analysis of framed structures under large displacement creep regimes is presented. The equilibrium equations of a prismatic and straight spatial beam element are formulated in the framework of corotational description, using the virtual work principle. Although the translations and rotations of the element are allowed to be large, the strains are assumed to be small. The material of a framed structure is assumed to be homogenous and isotropic. The bilinear elastic–plastic model with isotropic hardening and the power creep law are adopted for describing the inelastic behavior of the material. The numerical algorithm is implemented in a computer program called BMCA and its reliability is validated through test examples.

EFESTS: Educational finite element software for truss structure – Part 3: Geometrically nonlinear static analysis

2017 ◽  
Vol 45 (2) ◽  
pp. 154-169 ◽  
Author(s):  
Wenjie Zuo ◽  
Ke Huang ◽  
Fei Cheng
Keyword(s):  
Finite Element ◽  
Internal Force ◽  
Truss Structure ◽  
Nonlinear Static Analysis ◽  
Geometrically Nonlinear ◽  
Sequence Diagrams ◽  
Tangent Stiffness Matrix ◽  
Finite Element Software ◽  
Nonlinear Static ◽  
Internal Force Vector

This article covers the modeling, formulation, solution, and software development of the geometrically nonlinear static finite element method of truss structure. Firstly, we summarize the total Lagrange bar elment formulation, which includes the tangent stiffness matrix and the internal force vector. Secondly, static class diagrams and dynamic sequence diagrams assist students in designing software architecture. Thirdly, the analytical example of the 2-bar truss structure and the numerical example of the 10-bar truss structure are presented to promote students’ understanding of geometrically nonlinear finite element theory and application. Finally, the developed software is free for educational research and can be downloaded from the website: http://mach.jlu.edu.cn/hb_images/xygk/xssz_sz_js.php?id=395 .

scholarly journals AN EFFICIENT CO-ROTATIONAL FEM FORMULATION USING A PROJECTOR MATRIX

2016 ◽  
Vol 14 (2) ◽  
pp. 227 ◽  
Author(s):  
Viet Anh Nguyen ◽  
Manfred Zehn ◽  
Dragan Marinković
Keyword(s):  
Finite Elements ◽  
Deformation Gradient ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
Internal Force ◽  
Linear Analysis ◽  
Efficient Computation ◽  
Tangent Stiffness Matrix ◽  
Non Linear ◽  
Internal Force Vector

Co-rotational finite element (FE) formulations can be seen as a very efficient approach to resolving geometrically nonlinear problems in the field of structural mechanics. A number of co-rotational FE formulations have been well documented for shell and beam structures in the available literature. The purpose of this paper is to present a co-rotational FEM formulation for fast and highly efficient computation of large three-dimensional elastic deformations. On the one hand, the approach aims at a simple way of separating the element rigid-body rotation and the elastic deformational part by means of the polar decomposition of deformation gradient. On the other hand, a consistent linearization is introduced to derive the internal force vector and the tangent stiffness matrix based on the total Lagrangian formulation. It results in a non-linear projector matrix. In this way, it ensures the force equilibrium of each element and enables a relatively straightforward upgrade of the finite elements for linear analysis to the finite elements for geometrically non-linear analysis. In this work, a simple 4-node tetrahedral element is used. To demonstrate the efficiency and accuracy of the proposed formulation, nonlinear results from ABAQUS are used as a reference.

scholarly journals An Improved Analytical Algorithm on Main Cable System of Suspension Bridge

2018 ◽  
Vol 8 (8) ◽  
pp. 1358 ◽  
Author(s):  
Chuanxi Li ◽  
Jun He ◽  
Zhe Zhang ◽  
Yang Liu ◽  
Hongjun Ke ◽  
...  
Keyword(s):  
Search Algorithm ◽  
Suspension Bridge ◽  
Internal Force ◽  
Element Formulation ◽  
Cable System ◽  
Tangent Stiffness Matrix ◽  
Main Cable ◽  
Penalty Factor ◽  
Analytical Algorithm ◽  
Internal Force Vector

This paper develops an improved analytical algorithm on the main cable system of suspension bridge. A catenary cable element is presented for the nonlinear analysis on main cable system that is subjected to static loadings. The tangent stiffness matrix and internal force vector of the element are derived explicitly based on the exact analytical expressions of elastic catenary. Self-weight of the cables can be directly considered without any approximations. The effect of pre-tension of cable is also included in the element formulation. A search algorithm with the penalty factor is introduced to identify the initial components for convergence with high precision and fast speed. Numerical examples are presented and discussed to illustrate the accuracy and efficiency of the proposed analytical algorithm.

scholarly journals ANÁLISE QUALITATIVA DE SÓLIDOS ELASTOPLÁSTICOS SOB DEFORMAÇÃO FINITA UTILIZANDO ELEMENTOS DE BARRA BI-ARTICULADOS 2D E 3D

2016 ◽  
Vol 13 (1) ◽  
Author(s):  
William Taylor Matias Silva ◽  
Wellington Andrade Da Silva ◽  
Marcus Alexandre Noronha Brito
Keyword(s):  
Stiffness Matrix ◽  
Uniaxial Stress ◽  
Internal Force ◽  
Logarithmic Strain ◽  
Multiplicative Decomposition ◽  
Force Vector ◽  
Conjugate Pair ◽  
Tangent Stiffness Matrix ◽  
Internal Force Vector ◽  
2D And 3D

RESUMO: Neste trabalho apresenta-se uma descrição Lagrangeana Total para retratar sólidos elastoplásticos sob deformação finita. Discretiza-se estes sólidos com elementos de treliça 2D e 3D com o intuito de obter analiticamente o vetor de forças internas e a matriz de rigidez tangente. Assume-se um modelo constitutivo hiperelástico para o estado uniaxial de tensão-deformação, utilizando a tensão de Kirchhoff e a deformação logarítmica, que formam um par energeticamente conjugado. Para descrever as deformações plásticas finitas utiliza-se a hipótese da decomposição multiplicativa do estiramento uniaxial do elemento de treliça. Por fim, apresentam-se algumas simulações numéricas de sólidos 3D discretizados com elementos de treliça 2D e 3D. ABSTRACT: This paper presents a Lagrangian Total description to describe elastoplastic solids under finite deformation. These solids are discretized with truss elements 2D and 3D aiming to obtain analytically internal force vector and the tangent stiffness matrix. Are assumed a hyperelastic constitutive model for the state of uniaxial stress-strain using the Kirchhoff's stress and logarithmic strain, to form a conjugate pair energetically. To describe the finite plastic deformation using the hypothesis of the multiplicative decomposition of uniaxial stretching of the truss element. Finally, we present some numerical simulations of solid 3D discretized with 2D and 3D truss elements.

Performance of the Incremental and Non-Incremental Finite Element Formulations in Flexible Multibody Problems

1999 ◽  
Vol 122 (4) ◽  
pp. 498-507 ◽  
Author(s):  
Marcello Campanelli ◽  
Marcello Berzeri ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Multibody Systems ◽  
Absolute Nodal Coordinate Formulation ◽  
Flexible Multibody Systems ◽  
Large Displacement ◽  
Body Motion ◽  
Absolute Nodal Coordinate ◽  
Flexible Multibody ◽  
The Absolute ◽  
Finite Element Formulations

Many flexible multibody applications are characterized by high inertia forces and motion discontinuities. Because of these characteristics, problems can be encountered when large displacement finite element formulations are used in the simulation of flexible multibody systems. In this investigation, the performance of two different large displacement finite element formulations in the analysis of flexible multibody systems is investigated. These are the incremental corotational procedure proposed in an earlier article (Rankin, C. C., and Brogan, F. A., 1986, ASME J. Pressure Vessel Technol., 108, pp. 165–174) and the non-incremental absolute nodal coordinate formulation recently proposed (Shabana, A. A., 1998, Dynamics of Multibody Systems, 2nd ed., Cambridge University Press, Cambridge). It is demonstrated in this investigation that the limitation resulting from the use of the infinitesmal nodal rotations in the incremental corotational procedure can lead to simulation problems even when simple flexible multibody applications are considered. The absolute nodal coordinate formulation, on the other hand, does not employ infinitesimal or finite rotation coordinates and leads to a constant mass matrix. Despite the fact that the absolute nodal coordinate formulation leads to a non-linear expression for the elastic forces, the results presented in this study, surprisingly, demonstrate that such a formulation is efficient in static problems as compared to the incremental corotational procedure. The excellent performance of the absolute nodal coordinate formulation in static and dynamic problems can be attributed to the fact that such a formulation does not employ rotations and leads to exact representation of the rigid body motion of the finite element. [S1050-0472(00)00604-8]

Geometrical Stiffness of Thin-Walled I-Beam Element Based on Rigid-Beam Assemblage Concept

2012 ◽  
Vol 28 (1) ◽  
pp. 97-106 ◽  
Author(s):  
J. D. Yau ◽  
S.-R. Kuo
Keyword(s):  
Stiffness Matrix ◽  
Virtual Work ◽  
Bending Moment ◽  
Beam Element ◽  
Narrow Beam ◽  
Cross Sectional ◽  
Geometric Stiffness ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Thin Walled

ABSTRACTUsing conventional virtual work method to derive geometric stiffness of a thin-walled beam element, researchers usually have to deal with nonlinear strains with high order terms and the induced moments caused by cross sectional stress results under rotations. To simplify the laborious procedure, this study decomposes an I-beam element into three narrow beam components in conjunction with geometrical hypothesis of rigid cross section. Then let us adopt Yanget al.'s simplified geometric stiffness matrix [kg]12×12of a rigid beam element as the basis of geometric stiffness of a narrow beam element. Finally, we can use rigid beam assemblage and stiffness transformation procedure to derivate the geometric stiffness matrix [kg]14×14of an I-beam element, in which two nodal warping deformations are included. From the derived [kg]14×14matrix, it can take into account the nature of various rotational moments, such as semi-tangential (ST) property for St. Venant torque and quasi-tangential (QT) property for both bending moment and warping torque. The applicability of the proposed [kg]14×14matrix to buckling problem and geometric nonlinear analysis of loaded I-shaped beam structures will be verified and compared with the results presented in existing literatures. Moreover, the post-buckling behavior of a centrally-load web-tapered I-beam with warping restraints will be investigated as well.

scholarly journals An efficient numerical approach for simulating contact in origami assemblages

2019 ◽  
Vol 475 (2230) ◽  
pp. 20190366 ◽  
Author(s):  
Yi Zhu ◽  
Evgueni T. Filipov
Keyword(s):  
Numerical Approach ◽  
Internal Force ◽  
Contact Forces ◽  
Model Parameters ◽  
Full Potential ◽  
Stationary Potential ◽  
Contact Potential ◽  
Proposed Model ◽  
Approach Infinity ◽  
Internal Force Vector

Origami-inspired structures provide novel solutions to many engineering applications. The presence of self-contact within origami patterns has been difficult to simulate, yet it has significant implications for the foldability, kinematics and resulting mechanical properties of the final origami system. To open up the full potential of origami engineering, this paper presents an efficient numerical approach that simulates the panel contact in a generalized origami framework. The proposed panel contact model is based on the principle of stationary potential energy and assumes that the contact forces are conserved. The contact potential is formulated such that both the internal force vector and the stiffness matrix approach infinity as the distance between the contacting panel and node approaches zero. We use benchmark simulations to show that the model can correctly capture the kinematics and mechanics induced by contact. By tuning the model parameters accordingly, this methodology can simulate the thickness in origami. Practical examples are used to demonstrate the validity, efficiency and the broad applicability of the proposed model.

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