Static Analysis of Fe Discretized Structures With Bounded Uncertainties via Interval Method

2009 ◽  
Author(s):  
Nicola Impollonia ◽  
Giuseppe Muscolino
Keyword(s):  
Static Analysis ◽  
Interval Analysis ◽  
Stiffness Matrix ◽  
Probabilistic Method ◽  
Probabilistic Approach ◽  
Great Accuracy ◽  
Truss Structures ◽  
Interval Model ◽  
Global Stiffness Matrix ◽  
Bounded Uncertainties

The uncertainty presents in many engineering analysis is usually modeled by probabilistic approach. It is now largely recognized that the probabilistic approach often cannot be applied to describe structural uncertainty; indeed, it requires a wealth of data, often unavailable, to define the probability density function of the uncertainties. Alternatively non-probabilistic method can be adopted. In this framework, the interval model seems today the most suitable analytical tool. The interval model is derived from the interval analysis, in which the number is treated as an interval variable with lower and upper bounds. However, the application of the interval analysis in classical form can result in a severe overestimation of the uncertainty of the output. In this paper the limit of interval analysis is overcome by deriving an alternative solution, in the framework of linear static analysis of finite element modeled structures with uncertain-but-bounded parameters. The proposed procedure is based on the factorization of the elemental stiffness matrix following the unimodal components concept, which allows a non conventional assembly of the global stiffness matrix, and on the inversion of the assembled stiffness matrix by an interval-valued Sherman-Morrison formula. Numerical results on truss structures evidence the great accuracy of the proposed approach.

scholarly journals Analysis of Key Elements of Truss Structures Based on the Tangent Stiffness Method

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1008
Author(s):  
Jian Feng ◽  
Changtong Li ◽  
Yixiang Xu ◽  
Qian Zhang ◽  
Fang Wang ◽  
...  
Keyword(s):  
Stiffness Matrix ◽  
Progressive Collapse ◽  
Truss Structures ◽  
Specific Information ◽  
Tangent Stiffness ◽  
Collapse Resistance ◽  
The Matrix ◽  
Support Conditions ◽  
Global Stiffness Matrix ◽  
Progressive Collapse Analysis

In recent years, the topic of progressive structural collapse has received more attention around the world, and the study of element importance is the key to studying progressive collapse resistance. However, there are many elements in truss structures, making it difficult to predict their importance. The global stiffness matrix contains the specific information of the structure and singularity of the matrix can reflect the safety status of the structure, so it is useful to evaluate the key elements based on the global stiffness matrix for truss structures. In this paper, according to the tangent stiffness-based method for the element importance, the square pyramid grid was chosen as an example, and the distribution rules of key elements under different support conditions, stiffness distributions, and geometric parameters were studied. Then, three common symmetric grid forms, i.e., diagonal square pyramid grids, biorthogonal lattice grids, and biorthogonal diagonal lattice grids, were selected to investigate their importance indices of elements. The principle in this work can be utilized in progressive collapse analysis and safety assessment for spatial truss structures.

A New Method Tracing Load-Deflection Equilibrium Path of a Doubly Nonlinear Truss

2012 ◽  
Vol 166-169 ◽  
pp. 68-72
Author(s):  
Shu Tang Liu ◽  
Qi Liang Long
Keyword(s):  
Matrix Equation ◽  
Stiffness Matrix ◽  
Large Scale ◽  
New Method ◽  
Truss Structure ◽  
Equilibrium Path ◽  
Nodal Coordinates ◽  
Doubly Nonlinear ◽  
Global Stiffness Matrix

A new method tracing the load-deflection equilibrium path of a truss with doubly nonlinearity is proposed. The total global stiffness matrix equation has been formulated in terms of nodal coordinates, iteration formulations has been written through adopting a single control coordinate, so that an new method tracing the load-deflection equilibrium path has been proposed. Analysis results of Star dome truss and Schwedeler dome truss have shown that the proposed method is stable numerically, quick in convergence, high in degree of accuracy and easy in use. The proposed method can be used for large-scale truss structure.

scholarly journals Statistical Downscaling of Daily Wind Speed Variations

2014 ◽  
Vol 53 (3) ◽  
pp. 660-675 ◽  
Author(s):  
Megan C. Kirchmeier ◽  
David J. Lorenz ◽  
Daniel J. Vimont
Keyword(s):  
Wind Speed ◽  
Gamma Distribution ◽  
Large Scale ◽  
Probabilistic Method ◽  
Probabilistic Approach ◽  
Local Scale ◽  
Scale Parameters ◽  
Wind Speeds ◽  
Distribution Shape ◽  
Realistic Information

AbstractThis study presents the development of a method to statistically downscale daily wind speed variations in an extended Great Lakes region. A probabilistic approach is used, predicting a daily-varying probability density function (PDF) of local-scale daily wind speed conditioned on large-scale daily wind speed predictors. Advantages of a probabilistic method are that it provides realistic information on the variance and extremes in addition to information on the mean, it allows the autocorrelation of downscaled realizations to be tuned to match the autocorrelation of local-scale observations, and it allows flexibility in the use of the final downscaled product. Much attention is given to fitting the proper functional form of the PDF by investigating the observed local-scale wind speed distribution (predictand) as a function of the decile of the large-scale wind (predictor). It is found that the local-scale standard deviation and the local-scale shape parameter (from a gamma distribution) are nonconstant functions of the large-scale predictor. As such, a vector generalized linear model is developed to relate the large-scale and local-scale wind speeds. Maximum likelihood and cross validation are used to fit local-scale gamma distribution shape and scale parameters to the large-scale wind speed. The result is a daily-varying probability distribution of local-scale wind speed, conditioned on the large-scale wind speed.

OpenMp solvers for parallel finite element and meshless analyses

2014 ◽  
Vol 31 (1) ◽  
pp. 2-17 ◽  
Author(s):  
S.H. Ju
Keyword(s):  
Finite Element ◽  
Stiffness Matrix ◽  
Preconditioned Conjugate Gradient ◽  
Content Type ◽  
Minimum Requirement ◽  
Source Codes ◽  
Parallel Solution ◽  
Parallel Finite Element ◽  
Fortran 90 ◽  
Global Stiffness Matrix

Purpose – This paper develops C++ and Fortran-90 solvers to establish parallel solution procedures in a finite element or meshless analysis program using shared memory computers. The paper aims to discuss these issues. Design/methodology/approach – The stiffness matrix can be symmetrical or unsymmetrical, and the solution schemes include sky-line Cholesky and parallel preconditioned conjugate gradient-like methods. Findings – By using the features of C++ or Fortran-90, the stiffness matrix and its auxiliary arrays can be encapsulated into a class or module as private arrays. This class or module will handle how to allocate, renumber, assemble, parallelize and solve these complicated arrays automatically. Practical implications – The source codes can be obtained online at http//myweb.ncku.edu.tw/∼juju. The major advantage of the scheme is that it is simple and systematic, so an efficient parallel finite element or meshless program can be established easily. Originality/value – With the minimum requirement of computer memory, an object-oriented C++ class and a Fortran-90 module were established to allocate, renumber, assemble, parallel, and solve the global stiffness matrix, so that the programmer does not need to handle them directly.

Probabilistic Approach to the Assessment of the Depth of Soil Freezing

2016 ◽  
Author(s):  
Jerzy Antoni Żurański ◽  
Andrzej Sobolewski
Keyword(s):  
Soil Structure ◽  
Maximum Likelihood Method ◽  
Probabilistic Method ◽  
Probabilistic Approach ◽  
Climatic Conditions ◽  
The Other ◽  
Soil Freezing ◽  
Likelihood Method ◽  
Freezing Depth ◽  
Characteristic Values

The paper deals with the probabilistic method of the assessment of the depth of soil freezing. Annual (winter) maxima of the position of the zero centigrade temperature measured in the soil were approximated by Gumbel probability distribution. Its parameters were estimated using maximum likelihood method. Results received on the base of data from 2 meteorological stations and 30 years of observations, called as characteristic values of 50-year return period, refelect the influence of the climatic conditions on the freezing depth. On the other hand the soil structure and its conditions also play an important role in freezing. Nowadays they may be taken into account using correction coefficients. It is concluded that this methods is more precise than a method using so called air freezing index. Received results are not the same as given in the old Polish Standard. New analysis is currently being done.

scholarly journals A Probabilistic Approach to Phosphorus Speciation of Soils Using P K-edge XANES Spectroscopy with Linear Combination Fitting

Soil Systems ◽  
2020 ◽  
Vol 4 (2) ◽  
pp. 26 ◽  
Author(s):  
Jon Petter Gustafsson ◽  
Sabina Braun ◽  
J. R. Marius Tuyishime ◽  
Gbotemi A. Adediran ◽  
Ruben Warrinnier ◽  
...  
Keyword(s):  
Linear Combination ◽  
Probabilistic Method ◽  
Probabilistic Approach ◽  
Latin Hypercube Sampling ◽  
Energy Calibration ◽  
Strongly Correlated ◽  
Edge Structure ◽  
Common Technique ◽  
End Members ◽  
X Ray Absorption

A common technique to quantitatively estimate P speciation in soil samples is to apply linear combination fitting (LCF) to normalized P K-edge X-ray absorption near-edge structure (XANES) spectra. Despite the rapid growth of such applications, the uncertainties of the fitted weights are still poorly known. Further, there are few reports to what extent the LCF standards represent unique end-members. Here, the co-variance between 34 standards was determined and their significance for LCF was discussed. We present a probabilistic approach for refining the calculation of LCF weights based on Latin hypercube sampling of normalized XANES spectra, where the contributions of energy calibration and normalization to fit uncertainty were considered. Many of the LCF standards, particularly within the same standard groups, were strongly correlated. This supports an approach in which the LCF standards are grouped. Moreover, adsorbed phytates and monetite were well described by other standards, which puts into question their use as end-members in LCF. Use of the probabilistic method resulted in uncertainties ranging from 2 to 11 percentage units. Uncertainties in the calibrated energy were important for the LCF weights, particularly for organic P, which changed with up to 2.7 percentage units per 0.01 eV error in energy. These results highlight the necessity of careful energy calibration and the use of frequent calibration checks. The probabilistic approach, in which at least 100 spectral variants are analyzed, improves our ability to identify the most likely P compounds present in a soil sample, and a procedure for this is suggested in the paper.

FIXED GRID FINITE ELEMENT ANALYSIS FOR 3D STRUCTURAL PROBLEMS

2005 ◽  
Vol 02 (04) ◽  
pp. 569-586 ◽  
Author(s):  
MANUEL J. GARCÍA ◽  
MIGUEL A. HENAO ◽  
OSCAR E. RUIZ
Keyword(s):  
Structural Optimization ◽  
Material Properties ◽  
Stiffness Matrix ◽  
Computational Cost ◽  
Evolutionary Strategies ◽  
Two Dimensional ◽  
Additional Advantage ◽  
Fixed Grid ◽  
Structural Problems ◽  
Global Stiffness Matrix

Fixed Grid (FG) methodology was first introduced by García and Steven as an engine for numerical estimation of two-dimensional elasticity problems. The advantages of using FG are simplicity and speed at a permissible level of accuracy. Two-dimensional FG has been proved effective in approximating the strain and stress field with low requirements of time and computational resources. Moreover, FG has been used as the analytical kernel for different structural optimization methods as Evolutionary Structural Optimization, Genetic Algorithms (GA), and Evolutionary Strategies. FG consists of dividing the bounding box of the topology of an object into a set of equally sized cubic elements. Elements are assessed to be inside (I), outside (O) or neither inside nor outside (NIO) of the object. Different material properties assigned to the inside and outside medium transform the problem into a multi-material elasticity problem. As a result of the subdivision NIO elements have non-continuous properties. They can be approximated in different ways which range from simple setting of NIO elements as O to complex non-continuous domain integration. If homogeneously averaged material properties are used to approximate the NIO element, the element stiffness matrix can be computed as a factor of a standard stiffness matrix thus reducing the computational cost of creating the global stiffness matrix. An additional advantage of FG is found when accomplishing re-analysis, since there is no need to recompute the whole stiffness matrix when the geometry changes. This article presents CAD to FG conversion and the stiffness matrix computation based on non-continuous elements. In addition inclusion/exclusion of O elements in the global stiffness matrix is studied. Preliminary results shown that non-continuous NIO elements improve the accuracy of the results with considerable savings in time. Numerical examples are presented to illustrate the possibilities of the method.

Finite Geometrically Similar Element Method for Dynamic Problem of a Cracked Specimen

2008 ◽  
Vol 33-37 ◽  
pp. 375-380
Author(s):  
You Tang Li ◽  
Ping Ma ◽  
Yao Bing Wei
Keyword(s):  
Stiffness Matrix ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Layer By Layer ◽  
Inertia Matrix ◽  
Small Set ◽  
Global Stiffness Matrix ◽  
Similar Elements ◽  
Similar Element ◽  
Element Method

A group of geometrically similar elements is automatically generated layer by layer around the tip of crack. By taking advantage of the same stiffness and similar mass of similarly shaped elements, the combined stiffness matrix and combined inertia matrix in area can be expressed by the displacement row matrix of outer polygon. The global stiffness matrix will be obtained if the combined stiffness matrix and combined inertia matrix of area are assembled to those of another elements according to corresponding nodes. The small set of generalized coordinates can be obtained through solving the equation, and then the dynamic stress intensity factor of crack will be obtained. The three points bending with single crack and shearing model with double cracks in explosive loading were calculated with finite geometrically similar element method.

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