scholarly journals Rotation-Free Based Numerical Model for Nonlinear Analysis of Thin Shells

Buildings ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 657
Author(s):  
Hrvoje Smoljanović ◽  
Ivan Balić ◽  
Ante Munjiza ◽  
Viktor Hristovski
Keyword(s):  
Numerical Model ◽  
Finite Elements ◽  
Yield Criterion ◽  
Geometrical Nonlinearity ◽  
Time Integration ◽  
Triangular Element ◽  
Integration Scheme ◽  
Flow Rule ◽  
Thin Shells ◽  
Time Step

This paper presents a computationally efficient numerical model for the analysis of thin shells based on rotation-free triangular finite elements. The geometry of the structure in the vicinity of the observed triangular element is approximated through a controlled domain consisting of nodes of the observed finite element and nodes of three adjacent finite elements between which a second-order spatial polynomial is defined. The model considers large displacements, large rotations, small strains, and material and geometrical nonlinearity. Material nonlinearity is implemented by considering the von Mises yield criterion and the Levi-Mises flow rule. The model uses an explicit time integration scheme to integrate motion equations but an implicit radial returning algorithm to compute the plastic strain at the end of each time step. The presented numerical model has been embedded in the program Y based on the finite–discrete element method and tested on simple examples. The advantage of the presented numerical model is displayed through a series of analyses where the obtained results are compared with other results presented in the literature.

scholarly journals Investigation of Air Pocket Behavior in Pipelines Using Rigid Column Model and Contributions of Time Integration Schemes

Water ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 785
Author(s):  
Arman Rokhzadi ◽  
Musandji Fuamba
Keyword(s):  
Transient Flow ◽  
Time Integration ◽  
Driving Pressure ◽  
Implicit Time ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Time Step ◽  
Column Model ◽  
Integration Schemes ◽  
Backward Euler

This paper studies the air pressurization problem caused by a partially pressurized transient flow in a reservoir-pipe system. The purpose of this study is to analyze the performance of the rigid column model in predicting the attenuation of the air pressure distribution. In this regard, an analytic formula for the amplitude and frequency will be derived, in which the influential parameters, particularly, the driving pressure and the air and water lengths, on the damping can be seen. The direct effect of the driving pressure and inverse effect of the product of the air and water lengths on the damping will be numerically examined. In addition, these numerical observations will be examined by solving different test cases and by comparing to available experimental data to show that the rigid column model is able to predict the damping. However, due to simplified assumptions associated with the rigid column model, the energy dissipation, as well as the damping, is underestimated. In this regard, using the backward Euler implicit time integration scheme, instead of the classical fourth order explicit Runge–Kutta scheme, will be proposed so that the numerical dissipation of the backward Euler implicit scheme represents the physical dissipation. In addition, a formula will be derived to calculate the appropriate time step size, by which the dissipation of the heat transfer can be compensated.

scholarly journals Numerical modeling of reinforced concrete structures: static and dynamic analysis

2013 ◽  
Vol 66 (4) ◽  
pp. 425-430 ◽  
Author(s):  
Jorge Luis Palomino Tamayo ◽  
Armando Miguel Awruch ◽  
Inácio Benvegnu Morsch
Keyword(s):  
Reinforced Concrete ◽  
Numerical Model ◽  
Finite Elements ◽  
Dynamic Analysis ◽  
Time Integration ◽  
Great Accuracy ◽  
Constitutive Law ◽  
Published Data ◽  
Static And Dynamic Analysis ◽  
Plates And Shells

A numerical model using the Finite Element Method (FEM) for the nonlinear static and dynamic analysis of reinforced concrete (RC) beams, plates and shells is presented in this work. For this purpose, computer programs based on plasticity theory and with crack monitoring capabilities are developed. The static analysis of RC shells up to failure load is carried out using 9-node degenerated shell finite elements while 20-node brick finite elements are used for dynamic applications. The elasto-plastic constitutive law for concrete is coupled with a strain-rate sensitive model in order to take into account high loading rate effect when transient loading is intended. The implicit Newmark scheme with predictor and corrector phases is used for time integration of the nonlinear system of equations. In both cases, the steel reinforcement is considered to be smeared and represented by membrane finite elements. Various benchmark examples are solved with the present numerical model and comparisons with other published data are performed. For all examples, the path failure, collapse loads and failure mechanism is reproduced with great accuracy.

scholarly journals A Semi-Implicit Version of the MPAS-Atmosphere Dynamical Core

2015 ◽  
Vol 143 (9) ◽  
pp. 3838-3855 ◽  
Author(s):  
Steven Sandbach ◽  
John Thuburn ◽  
Danail Vassilev ◽  
Michael G. Duda
Keyword(s):  
Time Integration ◽  
Standard Test ◽  
Newton Iteration ◽  
Atmospheric Modeling ◽  
Implicit Time ◽  
Integration Scheme ◽  
Baroclinic Wave ◽  
Time Step ◽  
Integration Schemes ◽  
Helmholtz Problem

Abstract An important question for atmospheric modeling is the viability of semi-implicit time integration schemes on massively parallel computing architectures. Semi-implicit schemes can provide increased stability and accuracy. However, they require the solution of an elliptic problem at each time step, creating concerns about their parallel efficiency and scalability. Here, a semi-implicit (SI) version of the Model for Prediction Across Scales (MPAS) is developed and compared with the original model version, which uses a split Runge–Kutta (SRK3) time integration scheme. The SI scheme is based on a quasi-Newton iteration toward a Crank–Nicolson scheme. Each Newton iteration requires the solution of a Helmholtz problem; here, the Helmholtz problem is derived, and its solution using a geometric multigrid method is described. On two standard test cases, a midlatitude baroclinic wave and a small-planet nonhydrostatic gravity wave, the SI and SRK3 versions produce almost identical results. On the baroclinic wave test, the SI version can use somewhat larger time steps (about 60%) than the SRK3 version before losing stability. The SI version costs 10%–20% more per step than the SRK3 version, and the weak and strong scalability characteristics of the two versions are very similar for the processor configurations the authors have been able to test (up to 1920 processors). Because of the spatial discretization of the pressure gradient in the lowest model layer, the SI version becomes unstable in the presence of realistic orography. Some further work will be needed to demonstrate the viability of the SI scheme in this case.

A New Unconditionally Stable Time Integration Method for Analysis of Nonlinear Structural Dynamics

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
Ali Akbar Gholampour ◽  
Mehdi Ghassemieh ◽  
Mahdi Karimi-Rad
Keyword(s):  
Time Integration ◽  
Second Order ◽  
Numerical Dispersion ◽  
Computational Time ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Time Step ◽  
Similar Time ◽  
Unconditionally Stable ◽  
Average Acceleration

A new time integration scheme is presented for solving the differential equation of motion with nonlinear stiffness. In this new implicit method, it is assumed that the acceleration varies quadratically within each time step. By increasing the order of acceleration, more terms of the Taylor series are used, which are expected to have responses with better accuracy than the classical methods. By considering this assumption and employing two parameters δ and α, a new family of unconditionally stable schemes is obtained. The order of accuracy, numerical dissipation, and numerical dispersion are used to measure the accuracy of the proposed method. Second order accuracy is achieved for all values of δ and α. The proposed method presents less dissipation at the lower modes in comparison with Newmark's average acceleration, Wilson-θ, and generalized-α methods. Moreover, this second order accurate method can control numerical damping in the higher modes. The numerical dispersion of the proposed method is compared with three unconditionally stable methods, namely, Newmark's average acceleration, Wilson-θ, and generalized-α methods. Furthermore, the overshooting effect of the proposed method is compared with these methods. By evaluating the computational time for analysis with similar time step duration, the proposed method is shown to be faster in comparison with the other methods.

Newmark-Beta Method in Discrete Elastic Rods Algorithm to Avoid Energy Dissipation

2019 ◽  
Vol 86 (8) ◽  
Author(s):  
Weicheng Huang ◽  
Mohammad Khalid Jawed
Keyword(s):  
Energy Dissipation ◽  
Time Integration ◽  
Integration Scheme ◽  
Integration Step ◽  
Elastic Rods ◽  
Computationally Efficient ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Time Integration Scheme

Discrete elastic rods (DER) algorithm presents a computationally efficient means of simulating the geometrically nonlinear dynamics of elastic rods. However, it can suffer from artificial energy loss during the time integration step. Our approach extends the existing DER technique by using a different time integration scheme—we consider a second-order, implicit Newmark-beta method to avoid energy dissipation. This treatment shows better convergence with time step size, specially when the damping forces are negligible and the structure undergoes vibratory motion. Two demonstrations—a cantilever beam and a helical rod hanging under gravity—are used to show the effectiveness of the modified discrete elastic rods simulator.

Numerical Integration of Some Stiff Constitutive Models of Inelastic Deformation

1980 ◽  
Vol 102 (1) ◽  
pp. 92-96 ◽  
Author(s):  
Virendra Kumar ◽  
Mahesh Morjaria ◽  
Subrata Mukherjee
Keyword(s):  
Numerical Integration ◽  
Inelastic Deformation ◽  
Time Integration ◽  
Constitutive Models ◽  
Integration Scheme ◽  
Uniaxial Deformation ◽  
Time Step ◽  
One Step ◽  
Numerical Time Integration ◽  
Step Control

Several strategies for numerical time-integration of some stiff constitutive models of inelastic deformation are presented in this paper. Numerical results and comparisons are presented for the integration of one such model for the case of uniaxial deformation under various prescribed histories of stress or strain. A simple one step Euler type integration scheme with automatic time-step control, which can be easily adapted to the solution of multiaxial boundary value problems, appears promising.

Studies on the Accuracy Stability and Efficiency of a New Time Integration Scheme for Ballast Modeling Using the Discrete Element Method

2014 ◽  
Author(s):  
G. F. Mathews ◽  
R. L. Mullen ◽  
D. C. Rizos
Keyword(s):  
Particle Interaction ◽  
Time Integration ◽  
Discrete Element ◽  
Critical Discussion ◽  
Implicit Time ◽  
Integration Scheme ◽  
Computationally Efficient ◽  
Time Step ◽  
Central Difference ◽  
Time Integration Scheme

This paper presents the development of a semi-implicit time integration scheme, originally developed for structural dynamics in the 1970’s, and its implementation for use in Discrete Element Methods (DEM) for rigid particle interaction, and interaction of elastic bodies that are modeled as a cluster of rigid interconnected particles. The method is developed in view of ballast modeling that accounts for the flexibility of aggregates and the arbitrary shape and size of granules. The proposed scheme does not require any matrix inversions and is expressed in an incremental form making it appropriate for non-linear problems. The proposed method focuses on improving the efficiency, stability and accuracy of the solutions, as compared to current practice. A critical discussion of the findings of the studies is presented. Extended verification and assessment studies demonstrate that the proposed algorithm is unconditionally stable and accurate even for large time step sizes. It is demonstrated that the proposed method is at least as computationally efficient as the Central Difference Method. Guidelines for the implementation of the method to ballast modeling are discussed.

Modeling the damped dynamic behavior of a flexible pendulum

2019 ◽  
Vol 54 (2) ◽  
pp. 116-129 ◽  
Author(s):  
Roberto Ortega ◽  
Geraldine Farías ◽  
Marcela Cruchaga ◽  
Matías Rivero ◽  
Mariano Vázquez ◽  
...  
Keyword(s):  
High Speed ◽  
Time Integration ◽  
Integration Scheme ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Rayleigh Damping ◽  
Integration Schemes ◽  
Time Integration Schemes ◽  
Damping Model

The focus of this work is on the computational modeling of a pendulum made of a hyperelastic material and the corresponding experimental validation with the aim of contributing to the study of a material commonly used in seismic absorber devices. From the proposed dynamics experiment, the motion of the pendulum is recorded using a high-speed camera. The evolution of the pendulum’s positions is recovered using a capturing motion technique by tracking markers. The simulation of the problem is developed in the framework of a parallel multi-physics code. Particular emphasis is placed on the analysis of the Newmark integration scheme and the use of Rayleigh damping model. In particular, the time step size effect is analyzed. A strong time step size dependency is obtained for dissipative time integration schemes, while the Rayleigh damping formulation without time integration dissipation shows time step–independent results when convergence is achieved.

A Dissipative Momentum-Conserving Time Integration Algorithm for Nonlinear Structural Dynamics

2021 ◽  
pp. 2150116
Author(s):  
Salvatore Lopez
Keyword(s):  
Angular Momentum ◽  
Structural Dynamics ◽  
Time Integration ◽  
Integration Scheme ◽  
Second Phase ◽  
Time Step ◽  
Integration Algorithm ◽  
Nonlinear Structural Dynamics ◽  
Nonlinear Structural ◽  
Solution Point

A second-order accurate single-step time integration method for nonlinear structural dynamics is developed. The method combines algorithmic dissipation of higher modes and conservation of linear and angular momentum and is composed of two phases. In the first phase, a solution point is computed by a basic integration scheme, the generalized-[Formula: see text] method being adopted due to its higher level of high-frequency dissipation. In the second phase, a correction is hypothesized as a linear combination of the solution in the basic step and the gradient of vector components of the incremental linear and angular momentum. By solving a system composed of six linear equations, the searched for corrected solution in the time step is then provided. The novelty in the presented integration scheme lies in the way of imposing the conservation of linear and angular momentum. In fact, this imposition is carried out as a correction of the computed solution point in the time step and not through an enlarged system of equations of motion. To perform tests on plane and spatial motion of three-dimensional structural models, a small strains — finite rotations corotational formulation is also described.

Impact Analysis of Sandwich Composites

2008 ◽  
Author(s):  
Laura Ferrero ◽  
Ugo Icardi
Keyword(s):  
Impact Analysis ◽  
Time Integration ◽  
Nonlinear Problems ◽  
Implicit Time ◽  
Contact Radius ◽  
Integration Scheme ◽  
Sandwich Composites ◽  
Time Step ◽  
Wide Range ◽  
The Impact

A finite element simulation of impacts on sandwich composites with laminated faces is presented; it is based on a refined multilayered plate model with a high-order zig-zag representation of displacements, which is incorporated through a strain energy updating process. This allows the implementation into existing commercial finite elements codes, preserving their program structure. As customary, the Hertzian law and the Newmark implicit time integration scheme are used for solving the contact problem. The contact radius and the force are computed within each time step by an iterative algorithm which forces the impacted top surface to conform, in the least-squares sense, to the shape of the impactor. Nonlinear strains of von Karman type are used. As appearing by the comparison with experimental results, the present model is able to accurately predict the impact force, the core damage and the damage of face sheets in sandwich composites with foam and or honeycomb core. Moreover, this paper also assesses the accuracy and the range of application of stress based criteria in predicting the onset and evolution of delamination in service. These criteria are widespread by virtue of their low run time and storage costs, although no exhaustive proofs are known weather they are accurate enough for a reasonably wide range of applications. Since where highly iterative solutions are involved (e.g., impact and geometric, or material nonlinear problems) they are the only currently affordable failure models, it appears of primary importance to fill this gap. Aimed to contribute to the knowledge advancement in this field, a comparison is presented with more sophisticate fracture mechanics and progressive delamination models.

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