Numerical Methods in Structural Dynamics

1974 ◽  
Vol 1 (2) ◽  
pp. 179-193 ◽  
Author(s):  
J. L. Humar ◽  
E. W. Wright
Keyword(s):  
Numerical Integration ◽  
Structural Dynamics ◽  
Single Point ◽  
Computation Time ◽  
Point Method ◽  
Multiple Point ◽  
Considerable Saving ◽  
Random Forcing ◽  
Forcing Function ◽  
Predictor Corrector

The dynamic analysis of a structure subjected to a random forcing function from a source such as earthquake, blast, or wind requires the use of a numerical integration technique. The efficiency and accuracy of the technique employed is of great importance for both research and practical design. The more effective methods of numerical integration belong to the category designated as ‘predictor-corrector’ methods. A systematic method is presented for the derivation of single-point and multiple-point predictor-corrector formulae. It is shown that most of the methods of numerical integration presently employed in structural dynamics are single-point predictor-corrector methods. A scheme of iteration is usually employed for the solution of the difference equations obtained by the application of these methods. It is shown that for problems in structural dynamics, it is not necessary to use an iterative scheme; a process of elimination is feasible and also gives considerable economy in computation time. It is further shown that the choice of an appropriate multi-point method for the numerical integration of the equations of motion of an elastic system can lead to a considerable saving in computation time and cost. One such multi-point method is presented, and its truncation error and stability are examined.

Comparison of Pharmacokinetic Procedures for Dosing Lithium Based on Analysis of Prediction Error

1988 ◽  
Vol 22 (3) ◽  
pp. 227-231 ◽  
Author(s):  
Jerry L. Browne ◽  
Rajesh A. Patel ◽  
Camerson S. Huffman ◽  
Betty K. Hussey
Keyword(s):  
Steady State ◽  
Prediction Error ◽  
Lithium Concentration ◽  
Single Point ◽  
Lithium Carbonate ◽  
Point Method ◽  
Sign Test ◽  
Multiple Point ◽  
Prediction Errors ◽  
Dosing Method

Five pharmacokinetic methods for estimating maintenance dosage requirements of lithium carbonate were compared retrospectively in 20 inpatients with acute bipolar illness. Specific pharmacokinetic methods tested included the method of Cooper, the multiple-point method of Perry, the single-point method of Perry, the method of Zetin, and the method of Pepin. Data analysis was based on evaluation of prediction error or the difference between the predicted steady-state lithium concentration and the measured steady-state lithium concentration at equivalent daily doses. Each dosing method was assessed in regard to accuracy and bias of predicted steady-state serum lithium concentrations. Bias was assessed by comparison of the median value of the prediction error with zero. The dosing recommendation based on the Cooper nomogram resulted in a significant positive bias (p ≤ 0.05). Intermethod accuracy was assessed by comparison of the absolute prediction errors of each dosing method. Significant differences in accuracy were observed between the method of Pepin when compared with the single-point method of Perry (p ≤ 0.05, k-sample sign test). All other comparisons were nonsignificant.

scholarly journals Glomerular filtration rate determined from a single plasma sample after intravenous iohexol injection: is it reliable?

1996 ◽  
Vol 7 (12) ◽  
pp. 2689-2693
Author(s):  
F Gaspari ◽  
E Guerini ◽  
N Perico ◽  
L Mosconi ◽  
P Ruggenenti ◽  
...  
Keyword(s):  
Plasma Clearance ◽  
Plasma Sample ◽  
Single Point ◽  
Good Alternative ◽  
Point Method ◽  
Multiple Point ◽  
Significance Level ◽  
Study Results ◽  
Single Plasma Sample Method ◽  
Single Plasma

The iohexol injection plasma clearance method is a good alternative to the inulin clearance method for determination of GFR, but requires multiple blood samples. To avoid this, methods have been developed which derive GFR from a formula that uses a single plasma concentration of the tracer and anthropometric data. The aim of this study was to evaluate whether a single plasma sample taken after iohexol injection allows reliable estimation of GFR. In this study, results of single-point determination were compared with those obtained by multiple-point plasma clearance. The GFR of 686 outpatients with different degrees of renal function were recalculated by use of the Jacobsson formula. The optimum time for sampling was found at 10 h after injection of the marker for clearances < 40 mL/min per 1.73 m2, 4 h for clearances between 40 and 99 mL/min per 1.73 m2, and 3 h for clearances > 100 mL/min per 1.73 m2. Results documented that for 75% of the patients, the simplified technique gave an error between -5% to +5% in the evaluation of GFR; for the remaining 25% of the patients, prediction error ranged from -22% to +40%. Furthermore, despite a highly significant correlation between multiple-point iohexol clearance (six plasma samples) and the single-point method (Y = 0.968X + 1.704, r2 = 0.988), the regression intercept was statistically different from 0 and the standard error of the slope estimate established that 95% confidence interval did not include 1.0 (the line of identity), thus indicating that the model can be rejected by the data at a significance level of 0.05. Thus the single-plasma-sample method to determine GFR after radiocontrast injection does not represent a real advantage over the multiple-point method and may lead to unacceptable errors in GFR calculation.

A New Predictor-corrector Infeasible Interior-point Algorithm for Linear Optimization in aWide Neighborhood

2020 ◽  
Vol 177 (2) ◽  
pp. 141-156
Author(s):  
Behrouz Kheirfam
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Linear Optimization ◽  
Point Method ◽  
Central Path ◽  
Interior Point Algorithm ◽  
Positive Direction ◽  
Complexity Result ◽  
Infeasible Interior Point Method ◽  
Predictor Corrector

In this paper, we propose a Mizuno-Todd-Ye type predictor-corrector infeasible interior-point method for linear optimization based on a wide neighborhood of the central path. According to Ai-Zhang’s original idea, we use two directions of distinct and orthogonal corresponding to the negative and positive parts of the right side vector of the centering equation of the central path. In the predictor stage, the step size along the corresponded infeasible directions to the negative part is chosen. In the corrector stage by modifying the positive directions system a full-Newton step is removed. We show that, in addition to the predictor step, our method reduces the duality gap in the corrector step and this can be a prominent feature of our method. We prove that the iteration complexity of the new algorithm is 𝒪(n log ɛ−1), which coincides with the best known complexity result for infeasible interior-point methods, where ɛ > 0 is the required precision. Due to the positive direction new system, we improve the theoretical complexity bound for this kind of infeasible interior-point method [1] by a factor of n . Numerical results are also provided to demonstrate the performance of the proposed algorithm.

Comparison of spectral methods for the evaluation of Stokes integral  

2021 ◽  
Author(s):  
Avadh Bihari Narayan ◽  
Ashutosh Tiwari ◽  
Govind Sharma ◽  
Balaji Devaraju ◽  
Onkar Dikshit
Keyword(s):  
Boundary Value Problems ◽  
Numerical Integration ◽  
Spectral Methods ◽  
Boundary Value ◽  
Fundamental Equation ◽  
Computation Time ◽  
Spherical Approximation ◽  
Integration Technique ◽  
Gravity Measurements ◽  
Stokes Integral

&lt;p&gt;The spherical approximation of the fundamental equation of geodesy defines the boundary value problems. Stokes&amp;#8217;s integral provides the solution of boundary value problems that enables the computation of geoid from the properly reduced gravity measurements to the geoid. The stokes integral can be evaluated by brute-force numerical integration, spectral methods, and least-squares collocation. There is a trade-off between computation time and accuracy when we chose numerical integration technique or any spectral method. This research will compare time complexity and the accuracy of different spectral methods (1D-FFT, 2D-FFT, Multi-band FFT) and numerical integration technique for the region in the lower Himalaya, around Nainital, Uttarakhand, India.&amp;#160;&lt;/p&gt;

scholarly journals On the point-source approximation of earthquake dynamics

2014 ◽  
Vol 57 (3) ◽  
Author(s):  
Andrea Bizzarri
Keyword(s):  
Point Source ◽  
Seismic Waves ◽  
Single Point ◽  
Seismic Source ◽  
Transition Process ◽  
Point Sources ◽  
Multiple Point ◽  
Earthquake Dynamics ◽  
Planar Fault ◽  
Source Models

<p>The focus on the present study is on the point-source approximation of a seismic source. First, we compare the synthetic motions on the free surface resulting from different analytical evolutions of the seismic source (the Gabor signal (G), the Bouchon ramp (B), the Cotton and Campillo ramp (CC), the Yoffe function (Y) and the Liu and Archuleta function (LA)). Our numerical experiments indicate that the CC and the Y functions produce synthetics with larger oscillations and correspondingly they have a higher frequency content. Moreover, the CC and the Y functions tend to produce higher peaks in the ground velocity (roughly of a factor of two). We have also found that the falloff at high frequencies is quite different: it roughly follows ω<span><sup>−2</sup></span> in the case of G and LA functions, it decays more faster than ω<span><sup>−2</sup></span> for the B function, while it is slow than ω<span><sup>−1</sup></span> for both the CC and the Y solutions. Then we perform a comparison of seismic waves resulting from 3-D extended ruptures (both supershear and subshear) obeying to different governing laws against those from a single point-source having the same features. It is shown that the point-source models tend to overestimate the ground motions and that they completely miss the Mach fronts emerging from the supershear transition process. When we compare the extended fault solutions against a multiple point-sources model the agreement becomes more significant, although relevant discrepancies still persist. Our results confirm that, and more importantly quantify how, the point-source approximation is unable to adequately describe the radiation emitted during a real world earthquake, even in the most idealized case of planar fault with homogeneous properties and embedded in a homogeneous, perfectly elastic medium.</p>

scholarly journals A Note on the Asymptotic Behavior of the Heights in $b$-Tries for $b$ Large

10.37236/1517 ◽  
2000 ◽  
Vol 7 (1) ◽  
Author(s):  
Charles Knessl ◽  
Wojciech Szpankowski
Keyword(s):  
Asymptotic Behavior ◽  
Saddle Point ◽  
Generating Functions ◽  
Single Point ◽  
Extreme Value ◽  
Limiting Distribution ◽  
Point Method ◽  
Saddle Point Method ◽  
Numerical Verification ◽  
Height Distribution

We study the limiting distribution of the height in a generalized trie in which external nodes are capable to store up to $b$ items (the so called $b$-tries). We assume that such a tree is built from $n$ random strings (items) generated by an unbiased memoryless source. In this paper, we discuss the case when $b$ and $n$ are both large. We shall identify five regions of the height distribution that should be compared to three regions obtained for fixed $b$. We prove that for most $n$, the limiting distribution is concentrated at the single point $k_1=\lfloor \log_2 (n/b)\rfloor +1$ as $n,b\to \infty$. We observe that this is quite different than the height distribution for fixed $b$, in which case the limiting distribution is of an extreme value type concentrated around $(1+1/b)\log_2 n$. We derive our results by analytic methods, namely generating functions and the saddle point method. We also present some numerical verification of our results.

scholarly journals Early Morphologic Alterations in Renal Artery Wall and Renal Nerves in Response to Catheter-Based Renal Denervation Procedure in Sheep: Difference Between Single-Point and Multiple-Point Ablation Catheters

2017 ◽  
pp. 601-614 ◽  
Author(s):  
M. TÁBORSKÝ ◽  
D. RICHTER ◽  
Z. TONAR ◽  
T. KUBÍKOVÁ ◽  
A. HERMAN ◽  
...  
Keyword(s):  
Renal Artery ◽  
Resistant Hypertension ◽  
Renal Denervation ◽  
Single Point ◽  
Renal Tissue ◽  
Renal Nerves ◽  
Multiple Point ◽  
Renal Nerve ◽  
Jude Medical ◽  
Novel Strategy

Renal sympathetic hyperactivity is critically involved in hypertension pathophysiology; renal denervation (RDN) presents a novel strategy for treatment of resistant hypertension cases. This study assessed effects of two RDN systems to detect acute intravascular, vascular and peri-vascular changes in the renal artery, and renal nerve alterations, in the sheep. The procedures using a single-point or multi-point ablation catheters, Symplicity FlexTM, Medtronic versus EnligHTNTM, St. Jude Medical were compared; the intact contralateral kidneys served as controls. Histopathological and immunohistochemical assessments were performed 48 h after RDN procedures; the kidney and suprarenal gland morphology was also evaluated. Special staining methods were applied for histologic analysis, to adequately score the injury of renal artery and adjacent renal nerves. These were more pronounced in the animals treated with the multi-point compared with the single-point catheter. However, neither RDN procedure led to complete renal nerve ablation. Forty-eight hours after the procedure no significant changes in plasma and renal tissue catecholamines were detected. The morphologic changes elicited by application of both RDN systems appeared to be dependent on individual anatomical variability of renal nerves in the sheep. Similar variability in humans may limit the therapeutic effectiveness of RDN procedures used in patients with resistant hypertension.

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