Singularly perturbed solution for nonlinear equations of fourth order with two parameters

Chen, Lihua; Jia-Qi, Mo; Liu, Shu-de

doi:10.1007/s12204-008-0495-8

Cited by 3 publications

(3 citation statements)

References 12 publications

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“…It is different from that as ε/μ 2 → 0 (μ → 0) in Ref. [19]. The latter has two boundary layers near x = a.…”

Section: Boundary Layer Correctionmentioning

confidence: 63%

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A class of singular perturbation solutions to semilinear equations of fourth order

Jia-Qi

2009

Appl. Math. Mech.-Engl. Ed.

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A class of singularly perturbed boundary value problems for semilinear equations of fourth order with two parameters are considered. Under suitable conditions, using the method of lower and upper solutions, the existence and the asymptotic behavior of the solution to the boundary value problem are studied. In the present paper, the solution to the original singularly perturbed problem with two parameters has only one boundary layer.

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“…It is different from that as ε/μ 2 → 0 (μ → 0) in Ref. [19]. The latter has two boundary layers near x = a.…”

Section: Boundary Layer Correctionmentioning

confidence: 63%

“…Remark 1 Noting the asymptotic expansion (19), we know that there is only one boundary layer near x = a for the solution to the original problem (1)-(3) with two parameters as μ 2 /ε → 0 (ε → 0). It is different from that as ε/μ 2 → 0 (μ → 0) in Ref.…”

Section: Boundary Layer Correctionmentioning

confidence: 99%

A class of singular perturbation solutions to semilinear equations of fourth order

Jia-Qi

2009

Appl. Math. Mech.-Engl. Ed.

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“…The aforementioned numerical implementations are executed in the FEM code CORE3D programmed by our research team [55] in which the symmetric successive over relaxationpreconditioned conjugate gradient solver is used to solve the large linear system [56]. This program has already been validated by our previous researches [2,40] and has successfully served many hydropower projects including Xiaowan Dam [57] which is one of the most challenging hydraulic projects in China.…”

Section: Mesoscopic Simulation For Creep Related Issues Of Concretementioning

confidence: 99%

Approaches of concrete creep using mesomechanics: numerical simulation and predictive model

Wang

Chen

2019

Modelling Simul. Mater. Sci. Eng.

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Simulation and prediction of fully-aggregated concrete creep is a fairly crucial but complex task in civil engineering and material science due to the heterogeneity of concrete with mixture compositions. To investigate the contribution of each composition to the concrete creep and the relationship between the basic creep laws of concrete and mortar, a numerical concrete (NC) model on meso-scale is established with a 3D finite element algorithm taking into account aggregates, mortar matrix and the interfacial transition zone (ITZ). This NC model can emulate the complex mesostructure of concrete and calculate its creep by recurrence formulas without recording the history of stress in terms of the elastic aging creep theory. After being validated by existing laboratory experimental data, the proposed model is further employed to study the influential factors such as the content and elastic modulus of aggregate as well as the action of aggregates and mortar matrix via ITZ. Based on the numerical simulations and theoretical analysis, a new predictive model of concrete creep is finally proposed which is able to well interpret the dilution and restraint effects of aggregate and the interaction among compositions.

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Free Vibration Modeling and Computation of Reinforced Thermoplastic Pipe (RTP) Conveying Fluid in Off/Inshore Industry Applications

Abbas

Chen

et al. 2018

MATEC Web Conf.

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Reinforced Thermoplastic Pipe (RTP) is a composite material flexible pipe. Due to RTP superior behavior, it encouraged the industry for using to offshore and inshore applications. Marine risers and cross-country pipelines resting on elastic medium are slender flexible structures conveying fluid and exhibit complex dynamic behaviors. Therefore, it requires accurate dynamic modeling for prediction the vibration characteristics. Transfer Matrix Method for Multibody Systems (MSTMM) is one of the sophisticated methods that can be used efficiently to model large systems and calculate its vibration characteristics and dynamic responses. The size of matrices in MSTMM remains small regardless of the number of elements in the model. Having smaller matrix sizes helps to have less computational expense leading to a faster answer. Based on the MSTMM advantages and Euler-Bernoulli linear theory, transfer matrix of the pipe in both offshore and inshore industry applications is built-up for vibration analysis. Recursive eigenvalue search algorithm is used to determine the system frequencies. Numerical examples are performed to validate with those published in the open literature.

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Singularly perturbed solution for nonlinear equations of fourth order with two parameters

Abstract: A class of singularly perturbed boundary value problem for nonlinear equation of fourth order with two parameters is considered. Under suitable conditions, the existence and asymptotic behavior of solution for boundary value problem are studied using theory of differential inequalities.

Cited by 3 publications

References 12 publications

A class of singular perturbation solutions to semilinear equations of fourth order

A class of singular perturbation solutions to semilinear equations of fourth order

Approaches of concrete creep using mesomechanics: numerical simulation and predictive model

Free Vibration Modeling and Computation of Reinforced Thermoplastic Pipe (RTP) Conveying Fluid in Off/Inshore Industry Applications

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