Nonlinear Analysis for the Crack Control of SMA Smart Concrete Beam Based on a Bidirectional B-Spline QR Method

Li, Yan; Mo, Tian-Jing; Li, Shuang-bei; Liang, Qing-guo; Li, Jianping; Rong, Qin

doi:10.1155/2018/6092479

Cited by 2 publications

(2 citation statements)

References 28 publications

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“…e SFPM has been proved more advantageous than the FEMs in analyzing the nonlinear behaviors of plates and beams. Li et al [25] used a bidirectional B-spline QR method (BB-sQRM) to study the crack control of reinforced concrete beam, in which the plane model was discretized with a set of spline nodes along two directions. e results proved the high efficiency and low computational cost of this method.…”

Section: Introductionmentioning

confidence: 99%

A Spline Finite Point Method for Nonlinear Bending Analysis of FG Plates in Thermal Environments Based on a Locking-free Thin/Thick Plate Theory

Huang

et al. 2020

Mathematical Problems in Engineering

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A spline finite point method (SFPM) based on a locking-free thin/thick plate theory, which is suitable for analysis of both thick and thin plates, is developed to study nonlinear bending behavior of functionally graded material (FGM) plates with different thickness in thermal environments. In the proposed method, one direction of the plate is discretized with a set of uniformly distributed spline nodes instead of meshes and the other direction is expressed with orthogonal functions determined by the boundary conditions. The displacements of the plate are constructed by the linear combination of orthogonal functions and cubic B-spline interpolation functions with high efficiency for modeling. The locking-free thin/thick plate theory used by the proposed method is based on the first-order shear deformation theory but takes the shear strains and displacements as basic unknowns. The material properties of the FG plate are assumed to vary along the thickness direction following the power function distribution. By comparing with several published research studies based on the finite element method (FEM), the correctness, efficiency, and generality of the new model are validated for rectangular plates. Moreover, uniform and nonlinear temperature rise conditions are discussed, respectively. The effect of the temperature distribution, in-plane temperature force, and elastic foundation on nonlinear bending under different parameters are discussed in detail.

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Section: Introductionmentioning

confidence: 99%

A Spline Finite Point Method for Nonlinear Bending Analysis of FG Plates in Thermal Environments Based on a Locking-free Thin/Thick Plate Theory

Huang

et al. 2020

Mathematical Problems in Engineering

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“…The constitutive equation and damage evolution of each damage model also differ widely. It is not appropriate to describe the constitutive equations only by using elastic or plastic theory, nor is it to describe the fatigue damage constitutive equation by applying only one existing damage model directly [4,10,11].…”

Section: Introductionmentioning

confidence: 99%

A Research on Fatigue Damage Constitutive Equation of Asphalt Mixture

Sun

Fang

Fan

et al. 2018

Mathematical Problems in Engineering

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The laboratory investigations of fatigue damage constitutive equation of asphalt mixture were carried out by three-point bending fatigue tests. The three-point bending fatigue tests were performed at three levels of stress-strength ratio (SSR), temperature, and loading rate. The coupled multifactor (stress-strength ratio, temperature, and loading rate) fatigue life equation was established, which can well predict the fatigue life of the asphalt mixture. Both a damage model and a damage evolution equation have been established based on the E-N curve, which indicate that fatigue damage evolution is nonlinear and consists of three stages. The sensitivity analysis of damage model parameters indicates that each parameter has different effects on the three stages of damage evolution. Based on the researches above, the fatigue damage constitutive equations were finally built based on the σ-ε curves, which consist of two parts: the damage accumulation stage and the fatigue failure stage. The elasticity-power hardening model was used to describe the constitutive relation of damage accumulation stage. The elasticity-power hardening model and the Sidoroff damage model were used to describe the constitutive relation of damage failure stage. The constitutive equations can well characterize the fatigue damage performance of the asphalt mixtures under cyclic loading.

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Nonlinear Analysis for the Crack Control of SMA Smart Concrete Beam Based on a Bidirectional B-Spline QR Method

Cited by 2 publications

References 28 publications

A Spline Finite Point Method for Nonlinear Bending Analysis of FG Plates in Thermal Environments Based on a Locking-free Thin/Thick Plate Theory

A Spline Finite Point Method for Nonlinear Bending Analysis of FG Plates in Thermal Environments Based on a Locking-free Thin/Thick Plate Theory

A Research on Fatigue Damage Constitutive Equation of Asphalt Mixture

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