guideline for applications of finite element method …...therefore structural engineers preferred...

5th International Symposium on Advances in Civil and Environmental EngineeringPractises for Sustainable Development (ACEPS-2017)

Guideline for Applications of Finite Element Method inStructural Engineering

S.M.C.M.Randiligama1, R.G.S.N. Jayathilake1, K.K. Wijesundara1

1Department of Civil EngineeringFaculty of Engineering

University of PeradeniyaPeradeniyaSRI LANKA

E-mail: [email protected]

Abstract: In the modern society, construction industry has to analyse very complicated structures.Therefore structural engineers preferred to use finite element software than analytical methods fortheir analysis, because analytical methods are very time consuming and even impossible for theiranalysis.

Based on the above study suitable guidelines have been proposed to the structural engineers forstructural modelling.

Keywords: Displacement based finite element method, Guideline, Structural Engineering

1. INTRODUCTION

Figure 1 Main steps in DBFE procedure

Problems and limitations of finite element formulation of different elements had been identified whenassuming the displacement and when obtaining the stiffness matrix. Problems can be occurred due tothe assumption of wrong displacement function and use of numerical integration to obtain stiffnessmatrix. According to the scope, any complicated structure can be analysed using bar elements, frame

Constitutive law

Assume a displacement

function

Strain function

Stresses

Nodal displacements/

Forces

Compatibility Principle of Virtual

displacement

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elements, plane stress / strain elements, plate, shell and solid elements.Furthermore, analysing a structural system the different elements may have to be connected together. Elements are connected at the common nodes. As number of degree of freedom having at a node varying from element to element, there may be problems occurred in connecting different element into one structure [2]. The main objective of this study was to identify those drawbacks and propose guidelines to structural engineers by using h refinement through case studies. This study was limited to the linearly elastic behaviour of material.

2. METHODOLOGY

Figure 2 Methodology

3. CASE STUDIES

3.1. Modelling of Single Tapered Truss

A single tapered truss with rectangular cross section is considered in this study. Height (h) and width(b) for all case studies are remained in constant of 200 mm and 200 mm respectively. Height (a) isvaried from 0.05m to 0.15m in 0.025m intervals while length of the truss (L) is varied from 1m to 5m in1m intervals resulting 25 case studies. They were analysed by restraining all the degrees of freedomsat one end and applying an axial force at the free end for linearly elastic material behavior as shown infigure 3. The axial displacement at the free end is obtained by the analysis for each of the casestudies. Percentage errors were calculated by using the results obtain from the tapered element andvalues obtain from basic theories.

L

ah P

L

b

Methodology

Element Formulation Modelling

Assume Displacement Function Element Connectivity Problem

Position of Neutral Axis

Element Connectivity Problem



371

Figure 3 Single tapered truss


3.2. Modelling of Doubly Tapered Truss

1 2

Figure 4: Doubly tapered truss

3.3. Modelling of Curved Tapered Beam

Figure 5 Elevation of cantiliver curved tapered beam

3.4. Modelling of plate bending problem by using plate, shell and solidelements

3.4.1. Effect of span/depth ratio of the slab

L

ah P

L

b2b1

a

L

h

P

L1=6m

L2=3m

L3=4m

L4=4m

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3.4.2. Effect of shear locking of the slab

3.5. Modelling of Slab Panels

3.6.

Figure 7 Analysis of slab panel using shell and solid elements


Figure 8 Frame to solid connection

4. RESULTS AND DISCUSSION

4.1. Modelling of Single Tapered Truss

All the results obtained from the tapered option in sap2000 is tally with maximum 0.2% of errorpercentage with the actual results obtain by basic theories. In sap2000 tapered option is only limited

500 kN100

kN

400*400 mm2

column

2*2 m2

foundation

0.6 m

5 m Improvement

373


to the linear, quad Therefore it is not necessary to do the h-refinement for the single linear tapered truss element analysis.

4.2. Modelling of Doubly Tapered Truss

Figure 9 Selection of number of element for the double tapered truss.

4.3. Modelling of Curved Tapered Beams

th

th

Therefore, the curved tapered beams were analysed by increasing the number of elements. Resultswere compared by using theoretical solutions only considering flexural deformations. Figure 10 showsthe displacement deviation.

Figure 10 For b/a = 6 ,deviation percentage vs number of elements for curved tapered beam

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4.4. Modelling of Plate Bending Problem by Using Plate, Shell and Solid Elements

4.4.1. Effect of span/depth ratio of the slab

Figure 11 Effects of span/depth ratio for slabs

4.4.2. Effect of shear locking of the slab

Figure 12 Effects of shear locking

4.5. Modelling of Slab Panels

375


Figure 13 Effect of restrain conditions for Corner Slab

4.6. Element Connectivity Problem

Table 1 The deviation percentage of horizontal displacement with theoretical solutions

5. CONCLUSIONS

th

Table 2 Limits for span/depth ratio

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6. ACKNOWLEDGEMENT

7. REFERENCES

Knupp P. M., 2000, Achieving finite element mesh quality via optimization of the Jacobian matrix normand associated quantities- Part 1 a framework for surface mesh optimization, International journal fornumerical methods in engineering, Published by John Wiley and Sons, Ltd.

Shashikant T. More, Bindu R.S., May 2015, Effect of mesh size on finite element analysis of platestructure, International Journal of Engineering science and Innovative Technology, Volume 4, Issue 3,

Zienkiewicz O.C., Taylor R.L., Zhu J.Z., April 6, 2010, The Finite Element Method: Its Basis andFundamentals, Sixth Edition.

Carrera E., Migliorettiand F. , Petrolo M., 2011 Guidelines and Recommendations on the Use ofHigher Order Finite Elements for Bending Analysis of Plates, International Journal for ComputationalMethods in Engineering Science and Mechanics.

Rakowski J., December 1990, The Interpretation of the Shear Locking in Beam Elements, Article incomputers and structures.

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guideline for applications of finite element method …...therefore structural engineers preferred...

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