Subrata Kumar Mondal, Sangamesh Gondegaon and Hari Kumar Voruganti
This paper proposes a novel approach to impose the Neumann boundary condition for isogeometric analysis (IGA) of Euler–Bernoulli beam with 1-D formulation. The proposed method is…
Abstract
Purpose
This paper proposes a novel approach to impose the Neumann boundary condition for isogeometric analysis (IGA) of Euler–Bernoulli beam with 1-D formulation. The proposed method is for only IGA in which it is difficult to handle the Neumann boundary conditions. The control points of B-spline are equivalent to nodes in finite element method. With 1-D formulation, it is not possible to accommodate multiple degrees of freedom in IGA. This case arises in the analysis of beams. The paper aims to propose a way to work around this issue in a simple way.
Design/methodology/approach
Neumann boundary conditions, which are even-order derivatives (example: double derivative) of the primary variable, are inherently satisfied in the weak form. Boundary conditions with an odd number of derivatives (example: slope) are imposed with the introduction of a new penalty matrix.
Findings
The proposed method can impose a slope boundary condition for IGA of a beam using 1-D formulation.
Originality/value
From the literature, it can be observed that the beam is formulated in 1-D by considering it as either a rotation-free element or a 2-D formulation by considering shear strain along with the normal strain. The work represents 1-D formulation of a beam while considering the slope boundary condition, which is easy and effective to formulate, compared with the slope boundary conditions reported in previous works.
Details
Keywords
Subrata Das, Hiranmoy Mondal, Prabir Kumar Kundu and Precious Sibanda
The focus of the paper is only on the contributions toward the use of entropy generation of non-Newtonian Casson fluid over an exponential stretching sheet. The purpose of this…
Abstract
Purpose
The focus of the paper is only on the contributions toward the use of entropy generation of non-Newtonian Casson fluid over an exponential stretching sheet. The purpose of this paper is to investigate the entropy generation and homogeneous–heterogeneous reaction. Velocity and thermal slips are considered instead of no-slip conditions at the boundary.
Design/methodology/approach
Basic equations in form of partial differential equations are converted into a system of ordinary differential equations and then solved using the spectral quasi-linearization method (SQLM).
Findings
The validity of the model is established using error analysis. Variation of the velocity, temperature, concentration profiles and entropy generation against some of the governing parameters are presented graphically. It is to be noted that the increase in entropy generation due to increase in heterogeneous reaction parameter is due to the increase in heat transfer irreversibility. It is further noted that the Bejan number decreases with Brinkman number because increase in Brinkman number reduces the total entropy generation.
Originality/value
This paper acquires realistic numerical explanations for rapidly convergent temperature and concentration profiles using the SQLM. Convergence of the numerical solutions was monitored using the residual error of the PDEs. The resulting equations are then integrated using the SQLM. The influence of emergent flow, heat and mass transfer parameters effects are shown graphically.