NONLINEAR ELASTO-DYNAMIC ANALYSIS OF I-BEAMS CURVED IN-PLAN

2009 ◽  
Vol 09 (02) ◽  
pp. 213-241 ◽  
Author(s):  
R. EMRE ERKMEN ◽  
MARK A. BRADFORD
Keyword(s):  
Dynamic Equilibrium ◽  
Virtual Work ◽  
Numerical Models ◽  
Time History ◽  
Element Formulation ◽  
Nonlinear Behaviour ◽  
Equilibrium Equations ◽  
Geometric Nonlinearities ◽  
Initial Curvature ◽  
Straight Beam

The elastic response of curved beams subjected to moving vertical loads and dynamic loads is investigated. Incremental dynamic equilibrium equations are derived by using the principle of virtual work. Newmark's step-by-step procedure is adopted to discretise the dynamic equilibrium equations and obtain the time history response. Geometric nonlinearities due to large deflections and rotations are taken into account. A total Lagrangian finite element formulation is developed. The numerical models are compared with the existing analytical solutions and employed to show the effects of geometric nonlinearities as well as the initial curvature on the dynamic behaviour of curved I-beams. It is shown that the geometric nonlinearities are significant even for service loads. The nonlinear behaviour of a curved beam is substantially different from the nonlinear behaviour of a straight beam when the initial curvature is not small.

A Finite Element Formulation for the Analysis of Horizontally-Curved Thin-Walled Beams

2015 ◽  
Author(s):  
Ashkan Afnani ◽  
Vida Niki ◽  
R. Emre Erkmen
Keyword(s):  
Finite Element ◽  
Virtual Work ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Curved Beams ◽  
Equilibrium Equations ◽  
Rotation Tensor ◽  
Initial Curvature ◽  
Horizontally Curved ◽  
Thin Walled

In this study, a finite element formulation is developed for the elastic analysis of thin-walled curved beams. Using a second-order rotation tensor, the strains of the deformed configuration are calculated in terms of the displacement values and the initial curvature. The principle of virtual work is then used to obtain the nonlinear equilibrium equations, based on which a finite element beam formulation is developed. The accuracy of the method is confirmed through comparisons with test results and shell-type finite element formulations and other curved beam formulations from the literature. It is also shown that the results of the developed formulation are very accurate for cases where initial curvature is very large.

IN-PLANE NONLINEAR BEHAVIOUR OF CIRCULAR PINNED ARCHES WITH ELASTIC RESTRAINTS UNDER THERMAL LOADING

2006 ◽  
Vol 06 (02) ◽  
pp. 163-177 ◽  
Author(s):  
M. A. BRADFORD
Keyword(s):  
Closed Form ◽  
Thermal Loading ◽  
Virtual Work ◽  
Thermal Buckling ◽  
Nonlinear Behaviour ◽  
Principle Of Virtual Work ◽  
Equilibrium Equations ◽  
Structural Behaviour ◽  
Geometric Imperfection ◽  
Included Angle

This paper considers the nonlinear in-plane behaviour of a circular arch subjected to thermal loading only. The arch is pinned at its ends, with the pins being on roller supports attached to longitudinal elastic springs that model an elastic foundation, or the restraint provided by adjacent members in a structural assemblage. By using a nonlinear formulation of the strain-displacement relationship, the principle of virtual work is used to produce the differential equations of in-plane equilibrium, as well as the statical boundary conditions that govern the structural behaviour under thermal loading. These equations are solved to produce the equilibrium equations in closed form. The possibility of thermal buckling of the arch is addressed by considering an adjacent buckled equilibrium configuration, and the differential equilibrium equations for this buckled state are also derived from the principle of virtual work. It is shown that unless the arch is flat, in which case it replicates a straight column, thermal buckling of the arch in the plane of its curvature cannot occur, and the arch deflects transversely without bound in the elastic range as the temperature increases. The nonlinear behaviour of a flat arch (with a small included angle) is similar to that of a column with a small initial geometric imperfection under axial loading, while the nonlinearity and magnitude of the deflections decrease with an increase of the included angle at a given temperature. By using the closed form solutions for the problem, the influence of the stiffness of the elastic spring supports is considered, as is the attainment of temperature-dependent first yielding of a steel arch.

Transient Waves in Anisotropic Laminated Plates, Part 1: Theory

1991 ◽  
Vol 113 (2) ◽  
pp. 230-234 ◽  
Author(s):  
G. R. Liu ◽  
J. Tani ◽  
T. Ohyoshi ◽  
K. Watanabe
Keyword(s):  
Numerical Method ◽  
Fourier Transforms ◽  
Dynamic Equilibrium ◽  
Virtual Work ◽  
Laminated Plates ◽  
The Finite Element Method ◽  
Equilibrium Equations ◽  
Transient Waves ◽  
Plate Elements ◽  
Hybrid Numerical Method

A hybrid numerical method in which the finite element method and the method of Fourier transforms are combined is proposed for computing the transient waves in anisotropic laminated plates excited by impact loads. The anisotropic laminated plate is divided into N plate elements, and the principle of virtual work is used to develop approximate dynamic equilibrium equations for three- and two-dimensional problems. The displacement response is determined by employing the Fourier transformation and the modal analysis. This hybrid numerical method is straightforward and easy to use.

scholarly journals Validation of Fiber-Based Distributed Plasticity Approach for Steel Bracing Models

2015 ◽  
Vol 1 (2) ◽  
pp. 1-13 ◽  
Author(s):  
Alper Kanyilmaz
Keyword(s):  
Numerical Model ◽  
Nonlinear Analysis ◽  
Numerical Models ◽  
Hysteresis Loops ◽  
Computation Time ◽  
Experimental Result ◽  
Analysis Approach ◽  
Element Formulation ◽  
Nonlinear Behaviour ◽  
Modelling Approach

Nonlinear analysis approach is not anymore limited only to research purposes, but becoming more popular as a tool that can be used during design, thanks to the increased efficiency of computer software and hardware. An accurately calibrated numerical model may simulate the behaviour of buildings in a quite realistic way, which helps designers understand better the performance of their structures. However, the feasibility of the nonlinear analysis approach is limited by the complexity of the numerical model, and the aim of any researcher or engineer is to obtain the most useful information in a reasonable amount of time. This study focuses on the validation of a simplified numerical modelling approach to simulate the nonlinear behaviour of steel bracings. The paper presents a comparison between two different modelling approaches; a refined finite element model using volumetric elements, and fiber-based model using beam elements with distributed plasticity. The numerical models calibrated with the experimental result from existing literature, reproduce the behaviour of cold formed square, and hot rolled open section steel elements under inelastic cyclic loading. The hysteresis loops obtained from two models show that the accuracy obtained by simpler fiber-element formulation is quite close to the more refined volumetric model. Finally, in order to assess the accuracy of the fiber-based modelling approach to estimate the nonlinear cyclic response of full-scale braced frame configurations, two real scale frames are analysed, and the results are compared with the results of the experiments performed on the test frames. In terms of computation time and accuracy, distributed plasticity model is much more efficient, and can be a good option to perform nonlinear analysis of multi-level buildings, which would be quite cumbersome with volumetric modelling approach. This study has been realized thanks to the research fund received from European commission with the contract MEAKADO RFSR-CT-2013-00022.

Probabilistic multiscale modeling of fracture in heterogeneous materials and structures

2020 ◽  
Vol 86 (7) ◽  
pp. 45-54
Author(s):  
A. M. Lepikhin ◽  
N. A. Makhutov ◽  
Yu. I. Shokin
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Fracture Mechanics ◽  
Multiscale Modeling ◽  
Virtual Work ◽  
Numerical Models ◽  
Heterogeneous Materials ◽  
Heterogeneous Structure ◽  
Generalized Coordinates ◽  
Heterogeneous Structures

The probabilistic aspects of multiscale modeling of the fracture of heterogeneous structures are considered. An approach combining homogenization methods with phenomenological and numerical models of fracture mechanics is proposed to solve the problems of assessing the probabilities of destruction of structurally heterogeneous materials. A model of a generalized heterogeneous structure consisting of heterogeneous materials and regions of different scales containing cracks and crack-like defects is formulated. Linking of scales is carried out using kinematic conditions and multiscale principle of virtual forces. The probability of destruction is formulated as the conditional probability of successive nested fracture events of different scales. Cracks and crack-like defects are considered the main sources of fracture. The distribution of defects is represented in the form of Poisson ensembles. Critical stresses at the tops of cracks are described by the Weibull model. Analytical expressions for the fracture probabilities of multiscale heterogeneous structures with multilevel limit states are obtained. An approach based on a modified Monte Carlo method of statistical modeling is proposed to assess the fracture probabilities taking into account the real morphology of heterogeneous structures. A feature of the proposed method is the use of a three-level fracture scheme with numerical solution of the problems at the micro, meso and macro scales. The main variables are generalized forces of the crack propagation and crack growth resistance. Crack sizes are considered generalized coordinates. To reduce the dimensionality, the problem of fracture mechanics is reformulated into the problem of stability of a heterogeneous structure under load with variations of generalized coordinates and analysis of the virtual work of generalized forces. Expressions for estimating the fracture probabilities using a modified Monte Carlo method for multiscale heterogeneous structures are obtained. The prospects of using the developed approaches to assess the fracture probabilities and address the problems of risk analysis of heterogeneous structures are shown.

scholarly journals Dynamic Equilibrium Equations in Unified Mechanics Theory

2021 ◽  
Vol 2 (1) ◽  
pp. 63-80
Author(s):  
Noushad Bin Jamal Bin Jamal M ◽  
Hsiao Wei Lee ◽  
Chebolu Lakshmana Rao ◽  
Cemal Basaran
Keyword(s):  
Energy Loss ◽  
Entropy Generation ◽  
Equilibrium Equation ◽  
Dynamic Equilibrium ◽  
Free Vibration Analysis ◽  
Newtonian Mechanics ◽  
Equilibrium Equations ◽  
Time Coordinate ◽  
Proposed Model ◽  
Laws Of Thermodynamics

Traditionally dynamic analysis is done using Newton’s universal laws of the equation of motion. According to the laws of Newtonian mechanics, the x, y, z, space-time coordinate system does not include a term for energy loss, an empirical damping term “C” is used in the dynamic equilibrium equation. Energy loss in any system is governed by the laws of thermodynamics. Unified Mechanics Theory (UMT) unifies the universal laws of motion of Newton and the laws of thermodynamics at ab-initio level. As a result, the energy loss [entropy generation] is automatically included in the laws of the Unified Mechanics Theory (UMT). Using unified mechanics theory, the dynamic equilibrium equation is derived and presented. One-dimensional free vibration analysis with frictional dissipation is used to compare the results of the proposed model with that of a Newtonian mechanics equation. For the proposed entropy generation equation in the system, the trend of predictions is comparable with the reported experimental results and Newtonian mechanics-based predictions.

scholarly journals Experimental and Numerical Crack Initiation Analysis of the Compressor Blades Working in Resonance Conditions

2011 ◽  
Vol 2011 (3) ◽  
pp. 134-153
Author(s):  
Lucjan Witek
Keyword(s):  
Finite Element ◽  
Crack Initiation ◽  
Transverse Vibration ◽  
Numerical Models ◽  
Fatigue Behavior ◽  
Time History ◽  
Fatigue Properties ◽  
Compressor Blades ◽  
Blade Vibration ◽  
Number Of Cycles

Experimental and Numerical Crack Initiation Analysis of the Compressor Blades Working in Resonance ConditionsThis paper presents the results of a complex experimental and numerical crack initiation analysis of the helicopter turbo-engine compressor blades subjected to vibrations. A nonlinear finite element method was utilized to determine the stress state of the blade during the first mode of transverse vibration. In this analysis, the numerical models without defects as well as those with V-notches were defined. The quality of the numerical solution was checked by the convergence analysis. The obtained results were next used as an input data into crack initiation (ε-N) analyses performed for the load time history equivalent to one cycle of the transverse vibration. In the fatigue analysis, the different methods such as: Neuber elastic-plastic strain correction, linear damage summation and Palmgreen-Miner rule were utilized. As a result of ε-N analysis, the number of load cycles to the first fatigue crack appearing in the compressor blades was obtained. Moreover, the influence of the blade vibration amplitude on the number of cycles to the crack initiation was analyzed. Values of the fatigue properties of the blade material were calculated using the Baumel-Seeger and Muralidharan methods. The influence of both the notch radius and values of the UTS of the blade material on the fatigue behavior of the structure was also considered. In the last part of the work, the finite element results were compared with the results of experimental vibration HCF tests performed for the compressor blades.

Numerical analysis of kinematic response of single piles

2000 ◽  
Vol 37 (6) ◽  
pp. 1368-1382 ◽  
Author(s):  
Kevin J Bentley ◽  
M Hesham El Naggar
Keyword(s):  
Finite Element ◽  
Human Life ◽  
Free Field ◽  
Time History ◽  
Benchmark Problems ◽  
Soil Parameters ◽  
Nonlinear Behaviour ◽  
Pile Head ◽  
Element Mesh ◽  
Single Piles

Recent destructive earthquakes have highlighted the need for increased research into the revamping of design codes and building regulations to prevent further catastrophic losses in terms of human life and economic assets. The present study investigated the response of single piles to kinematic seismic loading using the three-dimensional finite element program ANSYS. The objectives of this study were (i) to develop a finite element model that can accurately model the kinematic soil–structure interaction of piles, accounting for the nonlinear behaviour of the soil, discontinuity conditions at the pile–soil interface, energy dissipation, and wave propagation; and (ii) to use the developed model to evaluate the kinematic interaction effects on the pile response with respect to the input ground motion. The static performance of the model was verified against exact available solutions for benchmark problems including piles in elastic and elastoplastic soils. The geostatic stresses were accounted for and radiating boundaries were provided to replicate actual field conditions. Earthquake excitation with a low predominant frequency was applied as an acceleration–time history at the base bedrock of the finite element mesh. To evaluate the effects of the kinematic loading, the responses of both the free-field soil (with no piles) and the pile head were compared. It was found that the effect of the response of piles in elastic soil was slightly amplified in terms of accelerations and Fourier amplitudes. However, for elastoplastic soil with separation allowed, the pile head response closely resembled the free-field response to the low-frequency seismic excitation and the range of pile and soil parameters considered in this study.Key words: numerical modelling, dynamic, lateral, piles, kinematic, seismic.

scholarly journals History, observation and mathematical models in the seismic analysis of the Valadier abutment area in the Colosseum

1995 ◽  
Vol 38 (5-6) ◽  
Author(s):  
G. Croci ◽  
D. D'Ayala ◽  
R. Liburdi
Keyword(s):  
Mathematical Models ◽  
Seismic Analysis ◽  
Numerical Models ◽  
Time History ◽  
Historical Records ◽  
Direct Integration ◽  
Structural Behaviour ◽  
Seismic Behaviour ◽  
Before And After ◽  
Xix Century

The present work aimed to outline the need to investigate different fields of research to interpret the structural behaviour of a monument as complex as the Colosseum. It is shown how defining the numerical models first. then refining them, followed by interpretation of results. is strictly linked with the inforination gathered from historical records and observation of the ~nonumenta s it is today. The study is confined to the area of the Valadier abutment. analysing its state and its seismic behaviour before and after the XIX century restoration using different ilumerical tools, from the elastic modal analysis to the non linear step by step time history direct integration. The procedure comparati\ely evaluates the reliability in the interpretation of the results and identifies future lines or research.

Dynamics Redesign of Marine Structures

1985 ◽  
Vol 29 (04) ◽  
pp. 285-295 ◽  
Author(s):  
Curtis J. Hoff ◽  
Michael M. Bernitsas
Keyword(s):  
Large Scale ◽  
Structural Changes ◽  
Dynamic Equilibrium ◽  
Degree Of Freedom ◽  
Attractive Alternative ◽  
Equilibrium Equations ◽  
Element Analysis ◽  
Solution Methods ◽  
Tower Model ◽  
Energy Equations

The dynamic response of a marine structure depends upon the exciting forces and the modal characteristics of the structure. Excessive vibratory response requires reduction of the exciting loads or redesign of the structure or both. In this paper the general redesign problem is formulated. It applies to large-scale structures and allows for large structural changes. Solution of the redesign problem is achieved through perturbation methods which are an attractive alternative to traditional trial-and-error methods. Perturbation solution methods are based on dynamic equilibrium equations or energy equations or both. A new method based on the energy equations which enforces the mode orthogonality conditions is developed and evaluated against all existing methods. Two test cases, a 191-degree-of-freedom two-dimensional ship model and a 810-degree-of-freedom offshore light tower model are used to compare the methods numerically. It is shown that the method developed in this paper can produce, with a single finite element analysis of the baseline system, a structure which satisfies within acceptable limits all nonconflicting design objectives.

Sign in / Sign up

Export Citation Format

Share Document