An unconditionally stable implicit time integration algorithm: Modified quartic B-spline method

Shojaee, Saeed; Rostami, Sobhan; Abbasi, Ali

doi:10.1016/j.compstruc.2015.02.030

Cited by 40 publications

(10 citation statements)

References 18 publications

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“…Therefore, these observations lead to the conclusion that in mechanical systems subjected to fast movements, higher-order accelerations, also known in the scientific literature as jerk, snap, crackle, and pop [5], are occurring. The notion of second-order and higher-order accelerations is of major importance in the field of theoretical mechanics, but significant developments in other fields of science were also noted: numerical analysis [6,7], control [8], differential equations [8], astronomy, astrophysics, and space physics [9][10][11][12][13], medicine [14,15], meteorology [16] and many more. The main purpose of this paper was not to conduct an exclusive kinematic study on higher-order accelerations.…”

Section: Introductionmentioning

confidence: 99%

A New Approach in Analytical Dynamics of Mechanical Systems

2020

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This paper presents a new approach to the advanced dynamics of mechanical systems. It is known that in the movements corresponding to some mechanical systems (e.g., robots), accelerations of higher order are developed. Higher-order accelerations are an integral part of higher-order acceleration energies. Unlike other research papers devoted to these advanced notions, the main purpose of the paper is to present, in a matrix form, the defining expressions for the acceleration energies of a higher order. Following the differential principle in generalized form (a generalization of the Lagrange–D’Alembert principle), the equations of the dynamics of fast-moving systems include, instead of kinetic energies, the acceleration energies of higher-order. To establish the equations which characterize both the energies of accelerations and the advanced dynamics, the following input parameters are considered: matrix exponentials and higher-order differential matrices. An application of a 5 d.o.f robot structure is presented in the final part of the paper. This is used to illustrate the validity of the presented mathematical formulations.

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Section: Introductionmentioning

confidence: 99%

A New Approach in Analytical Dynamics of Mechanical Systems

2020

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“…Also for solving this, Liu et al proposed a new implicit algorithm using the backward Euler formula and the composite time integral. To reduce the effect of the high‐frequency numerical energy dissipation, Shojaee et al suggested an unconditionally stable implicit algorithm based on the quadratic B‐spline function. Such an effect could be also controlled by optimizing the weighting coefficients in the integral .…”

Section: Introductionmentioning

confidence: 99%

A temporal hybrid dynamic integration algorithm strategy for inelastic time history analysis of high‐rise reinforced concrete structures under strong earthquakes

Ren

2019

Structural Design Tall Build

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Summary A complete earthquake time history analysis (THA) requires a stable, accurate, and efficient dynamic integration algorithm. It is not rare to encounter numerical divergence when some implicit algorithms are used to deal with severe materially or geometrically nonlinearities. For explicit algorithms, computational efficiency is always a major concern. A temporal hybrid dynamic algorithm (THDA) strategy, which is specialized in the inelastic THAs of high‐rise reinforced concrete (RC) structures experiencing severe plasticity development, is developed herein. A preliminary evaluation is carried out on three low‐rise structural models, that is, two frame structures and one wall‐frame structure, for each group of collected implicit algorithms and explicit algorithms. From the evaluation, four alternatives are generated for the subsequent detailed assessment. A general framework for the THDA is proposed and implemented on a finite element analytical platform. The four alternatives are assessed based on their performance on a high‐rise frame core‐tube RC structure. The assessment indicates that the proposed THDA strategy can give rise to a more compatible dynamic integration algorithm for the complete THAs of high‐rise building structures when they are experiencing severe damage. The concerns about the computational stability, accuracy, and efficiency of the dynamic algorithms can be well balanced by the THDA.

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“…In structural dynamic analysis, direct time integration algorithms are widely used to solve the motion equation [1]. Many researchers [2][3][4] have focused on the improvement of numerical properties of time integration algorithms, such as numerical stability, accuracy, numerical dissipation, and computational efficiency.…”

Section: Introductionmentioning

confidence: 99%

A Modified Precise Integration Method for Long-Time Duration Dynamic Analysis

Huang

2018

Mathematical Problems in Engineering

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This paper presents a modified Precise Integration Method (PIM) for long-time duration dynamic analysis. The fundamental solution and loading operator matrices in the first time substep are numerically computed employing a known unconditionally stable method (referred to as original method in this paper). By using efficient recursive algorithms to evaluate these matrices in the first time-step, the same numerical results as those using the original method with small time-step are obtained. The proposed method avoids the need of matrix inversion and numerical quadrature formulae, while the particular solution obtained has the same accuracy as that of the homogeneous solution. Through setting a proper value of the time substep, satisfactory accuracy and numerical dissipation can be achieved.

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An unconditionally stable implicit time integration algorithm: Modified quartic B-spline method

Cited by 40 publications

References 18 publications

A New Approach in Analytical Dynamics of Mechanical Systems

A New Approach in Analytical Dynamics of Mechanical Systems

A temporal hybrid dynamic integration algorithm strategy for inelastic time history analysis of high‐rise reinforced concrete structures under strong earthquakes

A Modified Precise Integration Method for Long-Time Duration Dynamic Analysis

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