On the Effectiveness of Higher-Order Terms in Refined Beam Theories

2010 ◽  
Vol 78 (2) ◽  
Author(s):  
Erasmo Carrera ◽  
Marco Petrolo
Keyword(s):  
Finite Element ◽  
Fourth Order ◽  
The Other ◽  
Governing Equations ◽  
Error Type ◽  
Stress Components ◽  
Higher Order Terms ◽  
Engineering Problems ◽  
Carrera Unified Formulation ◽  
Beam Theories

This work deals with refined theories for beams with an increasing number of displacement variables. Reference has been made to the asymptotic and axiomatic methods. A Taylor-type expansion up to the fourth-order has been assumed over the section coordinates. The finite element governing equations have been derived in the framework of the Carrera unified formulation (CUF). The effectiveness of each expansion term, that is, of each displacement variable, has been established numerically considering various problems (traction, bending, and torsion), several beam sections (square, annular, and airfoil-type), and different beam slenderness ratios. The accuracy of these theories have been evaluated for displacement and stress components at different points over the section and along the beam axis. Error-type parameters have been introduced to establish the role played by each generalized displacement variable. It has been found that the number of terms that have to be retained for each of the considered beam theories is closely related to the addressed problem; different variables are requested to obtain accurate results for different problems. It has, therefore, been concluded that the full implementation of CUF, retaining all the available terms, would avoid the need of changing the theory when a problem is changed (geometries and/or loading conditions), as what happens in most engineering problems. On the other hand, CUF could be used to construct suitable beam theories in view of the fulfillment of prescribed accuracies.

Computational Study of Streamfunction-Vorticity Formulation of Incompressible Flow and Heat Transfer Problems

2011 ◽  
Vol 52-54 ◽  
pp. 511-516 ◽  
Author(s):  
Arup Kumar Borah
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Boundary Conditions ◽  
Incompressible Flow ◽  
Computational Study ◽  
The Other ◽  
Governing Equations ◽  
Flow And Heat Transfer ◽  
Continuity Constraint ◽  
Transfer Problems

In this paper we have studied the streamfunction-vorticity formulation can be advantageously used to analyse steady as well as unsteady incompressible flow and heat transfer problems, since it allows the elimination of pressure from the governing equations and automatically satisfies the continuity constraint. On the other hand, the specification of boundary conditions for the streamfunction-vorticity is not easy and a poor evaluation of these conditions may lead to serious difficulties in obtaining a converged solution. The main issue addressed in this paper is the specification in the boundary conditions in the context of finite element of discretization, but approach utilized can be easily extended to finite volume computations.

scholarly journals Best theory diagrams for multilayered plates considering multifield analysis

2017 ◽  
Vol 28 (16) ◽  
pp. 2184-2205 ◽  
Author(s):  
M Cinefra ◽  
E Carrera ◽  
A Lamberti ◽  
M Petrolo
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Governing Equations ◽  
Equilibrium Equations ◽  
Material Parameters ◽  
Stress Components ◽  
Minimum Number ◽  
Multilayered Plates ◽  
Carrera Unified Formulation ◽  
Definition Of

This work presents the best theory diagrams (BTDs) for multilayered plates involved in multifield problems (mechanical, thermal and electrical). A BTD is a curve that reports the minimum number of terms of a refined model for a given accuracy. The axiomatic/asymptotic technique is employed in order to detect the relevant terms, and the error is computed with respect to an exact or quasi-exact solution. The models that belong to the BTDs are constructed by means of a genetic algorithm and the Carrera Unified Formulation (CUF). The CUF defines the displacement field as an expansion of the thickness coordinate. The governing equations are obtained in terms of few fundamental nuclei, whose form does not depend on the particular expansion order that is employed. The Navier closed-form solution has been adopted to solve the equilibrium equations. The analyses herein reported are related to plates subjected to multifield loads: mechanical, thermal and electrical. The aim of this study is to evaluate the influence of the type of the load in the definition of the BTDs. In addition, the influence of geometry, material parameters and displacement/stress components are considered. The results suggest that the BTD and the CUF can be considered as tools to evaluate any structural theory against a reference solution. In addition, it has been found that the BTD definition is influenced to a great extent by the type of load.

scholarly journals Some Real-Life Applications of a Newly Designed Algorithm for Nonlinear Equations and Its Dynamics via Computer Tools

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Amir Naseem ◽  
M. A. Rehman ◽  
Jihad Younis
Keyword(s):  
Fourth Order ◽  
Real Life ◽  
The Other ◽  
Complex Polynomials ◽  
Order Convergence ◽  
Computer Tools ◽  
Root Finding ◽  
Derivative Free ◽  
Engineering Problems ◽  
Ostrowski’S Method

In this article, we design a novel fourth-order and derivative free root-finding algorithm. We construct this algorithm by applying the finite difference scheme on the well-known Ostrowski’s method. The convergence analysis shows that the newly designed algorithm possesses fourth-order convergence. To demonstrate the applicability of the designed algorithm, we consider five real-life engineering problems in the form of nonlinear scalar functions and then solve them via computer tools. The numerical results show that the new algorithm outperforms the other fourth-order comparable algorithms in the literature in terms of performance, applicability, and efficiency. Finally, we present the dynamics of the designed algorithm via computer tools by examining certain complex polynomials that depict the convergence and other graphical features of the designed algorithm.

THE ROLE OF FINITE ELEMENT METHOD IN CIVIL ENGINEERING

2018 ◽  
Vol 5 (02) ◽  
Author(s):  
Er. Hardik Dhull
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Approximate Solution ◽  
Analytical Method ◽  
Civil Engineering ◽  
The Finite Element Method ◽  
Engineering Problems ◽  
Building Components ◽  
Element Method

The finite element method is a numerical method that is used to find solution of mathematical and engineering problems. It basically deals with partial differential equations. It is very complex for civil engineers to study various structures by using analytical method,so they prefer finite element methods over the analytical methods. As it is an approximate solution, therefore several limitationsare associated in the applicationsin civil engineering due to misinterpretationof analyst. Hence, the main aim of the paper is to study the finite element method in details along with the benefits and limitations of using this method in analysis of building components like beams, frames, trusses, slabs etc.

scholarly journals Finite element analysis of reinforced concrete deep beam with large opening

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Elsayed Ismail ◽  
Mohamed S. Issa ◽  
Khaled Elbadry
Keyword(s):  
Finite Element ◽  
Reinforced Concrete ◽  
Concrete Beams ◽  
Load Capacity ◽  
Reinforced Concrete Beams ◽  
The Other ◽  
Deep Beam ◽  
Web Openings ◽  
Design Load ◽  
Large Opening

Abstract Background A series of nonlinear finite element (FE) analyses was performed to evaluate the different design approaches available in the literature for design of reinforced concrete deep beam with large opening. Three finite element models were developed and analyzed using the computer software ATENA. The three FE models of the deep beams were made for details based on three different design approaches: (Kong, F.K. and Sharp, G.R., Magazine of Concrete Res_30:89-95, 1978), (Mansur, M. A., Design of reinforced concrete beams with web openings, 2006), and Strut and Tie method (STM) as per ACI 318-14 (ACI318 Committee, Building Code Requirements for Structural Concrete (ACI318-14), 2014). Results from the FE analyses were compared with the three approaches to evaluate the effect of different reinforcement details on the structural behavior of transfer deep beam with large opening. Results The service load deflection is the same for the three models. The stiffnesses of the designs of (Mansur, M. A., Design of reinforced concrete beams with web openings, 2006) and STM reduce at a load higher than the ultimate design load while the (Kong, F.K. and Sharp, G.R., Magazine of Concrete Res_30:89-95, 1978) reduces stiffness at a load close to the ultimate design load. The deep beam designed according to (Mansur, M. A., Design of reinforced concrete beams with web openings, 2006) model starts cracking at load higher than the beam designed according to (Kong, F.K. and Sharp, G.R., Magazine of Concrete Res_30:89-95, 1978) method. The deep beam detailed according to (Kong, F.K. and Sharp, G.R., Magazine of Concrete Res_30:89-95, 1978) and (Mansur, M. A., Design of reinforced concrete beams with web openings, 2006) failed due to extensive shear cracks. The specimen detailed according to STM restores its capacity after initial failure. The three models satisfy the deflection limit. Conclusion It is found that the three design approaches give sufficient ultimate load capacity. The amount of reinforcement given by both (Mansur, M. A., Design of reinforced concrete beams with web openings, 2006) and (Kong, F.K. and Sharp, G.R., Magazine of Concrete Res_30:89-95, 1978) is the same. The reinforcement used by the STM method is higher than the other two methods. Additional reinforcement is needed to limit the crack widths. (Mansur, M. A., Design of reinforced concrete beams with web openings, (2006)) method gives lesser steel reinforcement requirement and higher failure load compared to the other two methods.

Stress Analysis of Cement Concrete Pavement under Overweight Loads

2012 ◽  
Vol 446-449 ◽  
pp. 949-953
Author(s):  
Ya Ni Lu ◽  
Tao Li Xiao
Keyword(s):  
Finite Element ◽  
Regression Analysis ◽  
Finite Element Model ◽  
Element Model ◽  
Concrete Pavement ◽  
The Other ◽  
Tension Stress ◽  
Statistical Regression ◽  
Cement Concrete ◽  
Cement Concrete Pavement

Special load has produced serious damage to the concrete pavement because of the great gross weight and heavy axle load, but the present specification has not mentioned this kind of load. On this occasion, Several conditions of critical load are identified through ANSYS finite element model analysis and the formula through statistical regression analysis to the bottom maximum tension stress is drawn up. Which can not only guide the concrete pavement design under the special load but also the result may be referred by the other kinds of engineering.

Study on Load Stress of Lean Concrete Base in Asphalt Pavement

2012 ◽  
Vol 178-181 ◽  
pp. 1495-1498
Author(s):  
Li Jun Suo
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Asphalt Pavement ◽  
Element Model ◽  
Pavement Design ◽  
The Other ◽  
Three Dimension ◽  
Traffic Loading ◽  
Concrete Base

Load stress, which is caused by traffic loading, is important parameter used in the analysis of the new pavement design. In order to study the load stress of lean concrete base in the asphalt pavement, first of all, three–dimension finite element model of the asphalt pavement is established. The main objectives of the paper are investigated. One is calculation for load stress of lean concrete base, and the other is analysis for relationship between load stress of lean concrete base and parameters, such as thickness, modulus. The results show that load stress of lean concrete base decreases, decreases and increases with increase of base’s thickness, surface’s thickness and ratio of base’s modulus to foundation’s modulus respectively. So far as the traffic axle loading is concerned, it has a significant impact on load stress of lean concrete base, and it can be seen from results that when load is taken from 100kN to 220kN, load stress increases quickly with the increase of the traffic axle loading.

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