The Study of Explicit Scheme of Hybrid Stress-Function Element with Rotation Degrees of Freedom

2013 ◽  
Vol 353-356 ◽  
pp. 3220-3223
Author(s):  
Li Na Ge ◽  
Ge Tian ◽  
Ming Wu Yuan ◽  
Meng Yan Song ◽  
Xiang Rong Fu
Keyword(s):  
Degrees Of Freedom ◽  
Integration Method ◽  
Computational Cost ◽  
Element Model ◽  
Fundamental Solutions ◽  
Plane Elasticity ◽  
Explicit Scheme ◽  
Triangular Element ◽  
Triangular Area ◽  
Triangular Area Coordinates

A simple and efficient explicit scheme of triangular planar element with rotation degrees of freedom is proposed in this paper. The basic fundamental solutions of plane elasticity problem based on Airy stress functions are used as trial functions to construct triangular element with drilling degrees of freedom. During the construction of element model, the explicit expression of element stiffness matrix is deduced by means of triangular area coordinates integration method, instead of numerical integration method. Numerical calculation indicates that the element constructed in this paper is of high precision but less computational cost.

On Double Frequency Vibration of a Generator-Bearing System With Asymmetrical Stiffness

2002 ◽  
Author(s):  
Senlin Huang ◽  
Zhansheng Liu ◽  
Jiexian Su
Keyword(s):  
Degrees Of Freedom ◽  
Reduction Method ◽  
Integration Method ◽  
Element Model ◽  
Modal Interaction ◽  
Motion Equations ◽  
Double Frequency ◽  
Modal Reduction ◽  
Direct Integration Method ◽  
Bearing System

A finite element model for a generator-bearing system with asymmetrical stiffness is developed for investigation of the double frequency vibration. The modal reduction method is used for reducing the degrees of freedom system to improve computing efficiency, and the Newmark direct integration method is employed to solve the reduced motion equations. The two-modal interaction vibration is induced when the rotation speed is half a critical speed of the system due to asymmetry and gravity force of the generator. Such a phenomena is observed in the practical test.

Application of the Radial Integration Method into Dynamic Formulation of Anisotropic Shallow Shells Using Boundary Element Method

2014 ◽  
Vol 627 ◽  
pp. 465-468 ◽  
Author(s):  
L.J.M. Jesus ◽  
C.A. Cimini ◽  
E.L. Albuquerque
Keyword(s):  
Composite Laminate ◽  
Integration Method ◽  
Fundamental Solutions ◽  
Plane Elasticity ◽  
Boundary Integrals ◽  
Shallow Shells ◽  
Curvature Effects ◽  
Kirchhoff Plates ◽  
Dynamic Formulation ◽  
Computational Implementation

The formulation developed in this work is based on the coupling of plane elasticity formulation and thin plate formulation for plates (Kirchhoff plates). Both formulations use elastostatic fundamental solutions. Curvature effects are considered as body forces, which generates domain integrals. Domain integrals are transformed into boundary integrals using the radial integration method. Thus, only the boundary is discretized. A radial basis function is used as approximation function in domain integrals. The developed formulation is applied to the dynamic analysis of anisotropic and composite laminate shallow shells under time dependent loads. A computational implementation was performed for the formulation developed and results were compared with results from literature.

scholarly journals Multidisciplinary Optimisation of Aircraft Structures with Critical Non-Regular Areas: Current Practice and Challenges

Aerospace ◽  
2021 ◽  
Vol 8 (8) ◽  
pp. 223
Author(s):  
Massimo Sferza ◽  
Jelena Ninić ◽  
Dimitrios Chronopoulos ◽  
Florian Glock ◽  
Fernass Daoud
Keyword(s):  
Degrees Of Freedom ◽  
Computational Cost ◽  
Aircraft Design ◽  
Element Model ◽  
Main Role ◽  
Design Optimisation ◽  
Load Paths ◽  
Design Variables ◽  
Internal Deformation ◽  
Multidisciplinary Design Optimisation

The design optimisation of aerostructures is largely based on Multidisciplinary Design Optimisation (MDO), which is a set of tools used by the aircraft industry to size primary structures: wings, large portions of the fuselage or even an entire aircraft. The procedure is computationally expensive, as it must account for several thousands of loadcases, multiple analyses with hundreds of thousands of degrees of freedom, thousands of design variables and millions of constraints. Because of this, the coarse Global Finite Element Model (GFEM), on which the procedure is based, cannot be further refined. The structures represented in the GFEM contain many components and non-regular areas, which require a detailed modelling to capture their complex mechanical behaviour. Instead, in the GFEM, these components are represented by simplified models with approximated stiffness, whose main role is to contribute to the identification of the load paths over the whole structure. Therefore, these parts are kept fixed and are not constrained during the optimisation, as the description of their internal deformation is not sufficiently accurate. In this paper, we show that it would nevertheless be desirable to size the non-regular areas and the overall structures at once. Firstly, we introduce the concept of non-regular areas in the context of a structural airframe MDO. Secondly, we present a literature survey on MDO with a critical review of several architectures and their current applications to aircraft design optimisation. Then, we analyse and demonstrate with examples the possible consequences of neglecting non-regular areas when MDO is applied. In the conclusion, we analyse the requirements for alternative approaches and why the current ones are not viable solutions. Lastly, we discuss which characteristics of the problem could be exploited to contain the computational cost.

scholarly journals Substructure Interface Reduction Techniques to Capture Nonlinearities in Bolted Structures

2020 ◽  
Author(s):  
Aabhas Singh ◽  
Matthew S. Allen ◽  
Robert J. Kuether
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Model Updating ◽  
Computational Cost ◽  
Nonlinear Behavior ◽  
Element Model ◽  
System Level ◽  
Contact Interface ◽  
Single Node ◽  
Structural Dynamic

Abstract Structural dynamic finite element models typically use multipoint constraints (MPC) to condense the degrees of freedom (DOF) near bolted joints down to a single node, which can then be joined to neighboring structures with linear springs or nonlinear elements. Scalability becomes an issue when multiple joints are present in a system, because each requires its own model to capture the nonlinear behavior. While this increases the computational cost, the larger problem is that the parameters of the joint models are not known, and so one must solve a nonlinear model updating problem with potentially hundreds of unknown variables to fit the model to measurements. Furthermore, traditional MPC approaches are limited in how the flexibility of the interface is treated (i.e. with rigid bar elements the interface has no flexibility). To resolve this shortcoming, this work presents an alternative approach where the contact interface is reduced to a set of modal DOF which retain the flexibility of the interface and are capable of modeling multiple joints simultaneously. Specifically, system-level characteristic constraint (S-CC) reduction is used to reduce the motion at the contact interface to a small number of shapes. To capture the hysteresis and energy dissipation that is present during microslip of joints, a hysteretic element is applied to a small number of the S-CC Shapes. This method is compared against a traditional MPC method (using rigid bar elements) on a two-dimensional finite element model of a cantilever beam with a single joint near the free end. For all methods, a four-parameter Iwan element is applied to the interface DOF to capture how the amplitude dependent modal frequency and damping change with vibration amplitude.

Computationally Efficient Analysis of SMA Sensory Particles Embedded in Complex Aerostructures Using a Substructure Approach

2015 ◽  
Author(s):  
Brent Bielefeldt ◽  
Jacob Hochhalter ◽  
Darren Hartl
Keyword(s):  
Structural Damage ◽  
Degrees Of Freedom ◽  
Crack Detection ◽  
Computational Models ◽  
Fatigue Cracks ◽  
Computational Cost ◽  
Computation Time ◽  
Element Model ◽  
Aircraft Wing ◽  
Digital Twin

The Digital Twin concept represents an innovative method to monitor and predict the performance of an aircraft’s various subsystems. By creating ultra-realistic multi-physical computational models associated with each unique aircraft and combining them with known flight histories, operators could benefit from a real-time understanding of the vehicle’s current capabilities. One important facet of the Digital Twin program is the detection and monitoring of structural damage. Recently, a method to detect fatigue cracks using the transformation response of shape memory alloy (SMA) particles embedded in the aircraft structure has been proposed. By detecting changes in the mechanical and/or electromagnetic responses of embedded particles, operators could detect the onset of fatigue cracks in the vicinity of these particles. In this work, the development of a finite element model of an aircraft wing containing embedded SMA particles in key regions will be discussed. In particular, this model will feature a technique known as substructure analysis, which retains degrees of freedom at specified points key to scale transitions, greatly reducing computational cost. By using this technique to model an aircraft wing subjected to loading experienced during flight, we can simulate the response of these localized particles while also reducing computation time. This new model serves to demonstrate key aspects of this detection technique. Future work, including the determination of the material properties associated with these particles as well as exploring the positioning of these particles for optimal crack detection, is also discussed.

Driving Torsion Scans with Wavefront Propagation

2020 ◽  
Author(s):  
Yudong Qiu ◽  
Daniel Smith ◽  
Chaya Stern ◽  
mudong feng ◽  
Lee-Ping Wang
Keyword(s):  
Potential Energy ◽  
Force Field ◽  
Degrees Of Freedom ◽  
Computational Cost ◽  
Initial Guess ◽  
Field Development ◽  
Force Field Development ◽  
Wavefront Propagation ◽  
Open Source Software Package

<div>The parameterization of torsional / dihedral angle potential energy terms is a crucial part of developing molecular mechanics force fields.</div><div>Quantum mechanical (QM) methods are often used to provide samples of the potential energy surface (PES) for fitting the empirical parameters in these force field terms.</div><div>To ensure that the sampled molecular configurations are thermodynamically feasible, constrained QM geometry optimizations are typically carried out, which relax the orthogonal degrees of freedom while fixing the target torsion angle(s) on a grid of values.</div><div>However, the quality of results and computational cost are affected by various factors on a non-trivial PES, such as dependence on the chosen scan direction and the lack of efficient approaches to integrate results started from multiple initial guesses.</div><div>In this paper we propose a systematic and versatile workflow called \textit{TorsionDrive} to generate energy-minimized structures on a grid of torsion constraints by means of a recursive wavefront propagation algorithm, which resolves the deficiencies of conventional scanning approaches and generates higher quality QM data for force field development.</div><div>The capabilities of our method are presented for multi-dimensional scans and multiple initial guess structures, and an integration with the MolSSI QCArchive distributed computing ecosystem is described.</div><div>The method is implemented in an open-source software package that is compatible with many QM software packages and energy minimization codes.</div>

A Two-Dimensional Linear Assumed Strain Triangular Element for Finite Deformation Analysis

2005 ◽  
Vol 73 (6) ◽  
pp. 970-976 ◽  
Author(s):  
Fernando G. Flores
Keyword(s):  
Finite Deformation ◽  
Degrees Of Freedom ◽  
Yield Function ◽  
Triangular Element ◽  
Deformation Analysis ◽  
Elastic Model ◽  
Stress Strain ◽  
Metric Tensor ◽  
Assumed Strain ◽  
Non Linear

An assumed strain approach for a linear triangular element able to handle finite deformation problems is presented in this paper. The element is based on a total Lagrangian formulation and its geometry is defined by three nodes with only translational degrees of freedom. The strains are computed from the metric tensor, which is interpolated linearly from the values obtained at the mid-side points of the element. The evaluation of the gradient at each side of the triangle is made resorting to the geometry of the adjacent elements, leading to a four element patch. The approach is then nonconforming, nevertheless the element passes the patch test. To deal with plasticity at finite deformations a logarithmic stress-strain pair is used where an additive decomposition of elastic and plastic strains is adopted. A hyper-elastic model for the elastic linear stress-strain relation and an isotropic quadratic yield function (Mises) for the plastic part are considered. The element has been implemented in two finite element codes: an implicit static/dynamic program for moderately non-linear problems and an explicit dynamic code for problems with strong nonlinearities. Several examples are shown to assess the behavior of the present element in linear plane stress states and non-linear plane strain states as well as in axi-symmetric problems.

An accurate method to include lubrication forces in numerical simulations of dense Stokesian suspensions

2015 ◽  
Vol 769 ◽  
pp. 369-386 ◽  
Author(s):  
A. Lefebvre-Lepot ◽  
B. Merlet ◽  
T. N. Nguyen
Keyword(s):  
Short Range ◽  
Degrees Of Freedom ◽  
Computational Cost ◽  
Parameter Tuning ◽  
Accurate Method ◽  
Spherical Particles ◽  
Particle Model ◽  
Stokesian Dynamics ◽  
New Feature ◽  
The Many

We address the problem of computing the hydrodynamic forces and torques among $N$ solid spherical particles moving with given rotational and translational velocities in Stokes flow. We consider the original fluid–particle model without introducing new hypotheses or models. Our method includes the singular lubrication interactions which may occur when some particles come close to one another. The main new feature is that short-range interactions are propagated to the whole flow, including accurately the many-body lubrication interactions. The method builds on a pre-existing fluid solver and is flexible with respect to the choice of this solver. The error is the error generated by the fluid solver when computing non-singular flows (i.e. with negligible short-range interactions). Therefore, only a small number of degrees of freedom are required and we obtain very accurate simulations within a reasonable computational cost. Our method is closely related to a method proposed by Sangani & Mo (Phys. Fluids, vol. 6, 1994, pp. 1653–1662) but, in contrast with the latter, it does not require parameter tuning. We compare our method with the Stokesian dynamics of Durlofsky et al. (J. Fluid Mech., vol. 180, 1987, pp. 21–49) and show the higher accuracy of the former (both by analysis and by numerical experiments).

Finite Element Analysis of 2-D Structures by New Strain Based Triangular Element

2018 ◽  
Vol 35 (3) ◽  
pp. 305-313 ◽  
Author(s):  
C. Rebiai
Keyword(s):  
Dynamic Analysis ◽  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
Time Integration ◽  
Triangular Element ◽  
Membrane Element ◽  
Lumped Mass ◽  
Element Analysis ◽  
Benchmark Tests ◽  
Three Degrees Of Freedom

ABSTRACTIn this investigation, a new simple triangular strain based membrane element with drilling rotation for 2-D structures analysis is proposed. This new numerical model can be used for linear and dynamic analysis. The triangular element is named SBTE and it has three nodes with three degrees of freedom at each node. The displacements field of this element is based on the assumed functions for the various strains satisfying the compatibility equations. This developed element passed both patch and benchmark tests in the case of bending and shear problems. For the dynamic analysis, lumped mass with implicit/explicit time integration are employed. The obtained numerical results using the developed element converge toward the analytical and numerical solutions in both analyses.

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