UNIT 1 INTRODUCTION 1. What is meant meant by by finit finitee elem element ent? ? A small units having definite shape of geometry and nodes is called finite element. 2. Wh What at is is mean meantt by node node or joint? joint? Each kind of finite element has a specific structural shape and is inter- connected with the adjacent element by nodal point or nodes. At the nodes, degrees of freedom are located. The forces will act only at nodes at any others place in the element. 3. What is is the basi basi of finit finitee elemen elementt method method? ? Discretiation is the basis of finite element method. The art of subdividing a structure in to convenient number of smaller components is known as discretiation. !. What are the ty"e ty"ess of bo#nd bo#ndary ary ondi onditio tions? ns? a! "rima "rimary ry boun boundar dary y condi conditio tions ns b! #econdary boundary boundary conditions conditions $. %tate %tate the meth methods ods of en&i en&inee neerin rin& & analysi analysis? s? a! E$pe E$peri rime ment ntal al meth method odss b! Analytical methods c! %umerica %umericall method methodss or appro$im appro$imate ate methods methods '. What are the ty"es ty"es of elemen element? t? a! &D el element b! 'D element c! (D el element (. %tate the thre threee "hases "hases of finite finite element element method. method. a! "rep "repro roce cess ssin ing g b! Analysis c! "ost "ost "ro "roce cess ssin ing g ). Wh What at is str str# #t# t#ra rall "rob "roble lem? m? Displacement at each nodal point is obtained. )y these displacements solution stress and strain in each element can be calculated. *. What is non str#t str#t#ra #rall "ro "roble blem? m? Temperature Temperature or fluid pressure at each nodal point is obtained. )y using these values properties such as heat flow, fluid flow for each element can be calculated. 1+. What are the methods are are &enerally assoiated ,ith ,ith the finite element element analysis? a! *orce orce meth ethod b! Displacement Displacement or stiffness stiffness method. 11. 11. -"lain -"lain stiffness stiffness method. Displace Displacement ment or stiffne stiffness ss method, method, displacement displacement of the nodes is consider considered ed as the unknown unknown of the problem. Among Among them two approaches, approaches, displacement displacement method is desirable. desirable. 12. What is meant meant by "ost "roe "roessin& ssin&? ? Analysis and evaluation of the solution result is referred to as post processing. "ostprocessor computer program help the the user to interpret the the result by displaying displaying them in graphical form. form. 13. Name the /ariational /ariational methods. methods. &. +it it me metho thod. '. +ay+ay-e eig igh h +it +it met metho hod. d. 1!. What is meant meant by de&rees de&rees of freedom? freedom? hen the force or reaction act at nodal point node is subjected to deformation. The deformation includes displacement rotation, rotation, and or strains. These are collectively known as degrees of freedom 1$. What is meant by disreti0at disreti0ation ion and assembla&e? assembla&e? The art of subdiv subdividi iding ng a struct structure ure in to conve convenie nient nt numbe numberr of small smaller er compon componen ents ts is know known n as discreti discretiatio ation. n. These These smaller smaller compone components nts are then put together together.. The process process of uniting uniting the various various elements together is called assemblage. 1'. What is Raylei&h Raylei&hRit0 Rit0 method? method? t is integral approach method which is useful for solving comple$ structural problem, encountered in finite element analysis. This method is possible only if a suitable function is available. 1(. What is s"et s"et ratio? ratio? t is defined as the ratio of the largest dimension of the element to the smallest dimension. n many cases, as the aspect ratio increases the in accuracy of the solution increases. The conclusion conclusion of many researches is that the aspect ratio should be close to unity as possible. 1). What is is tr#ss tr#ss element? element? The truss elements are the part of a truss structure linked together by point joint which transmits only a$ial force to the element. 1*. What are the h and " /ersions /ersions of finite element method? t is used to improve the accuracy of the finite element method. n h version, the order of polynomial appro$imation for all elements is kept constant and the numbers of elements are increased. n p version, the numbers of elements are maintained constant and the order of polynomial appro$imation of element is increased. 2+. Name the ,ei&hted ,ei&hted resid#al resid#al method oint olloation method a! #ub domain collocation method b! east s/uares method method c! 0alerkins method.
UNIT 2 DI%CR-T- -4-5-NT%
1. 4ist the t,o ad/anta&es of "ost "roessin&. +e/uired result can be obtained in graphical form. 1ontour diagrams can be used to understand the solution easily and /uickly. 2. D#rin& disreti0ation6 mention the "laes ,here it is neessary to "lae a node? 1oncentrated load acting point, 1ross-section changing point Different material interjections #udden change in point load 3. What is the differene bet,een stati and dynami analysis? #tatic analysis2 The solution of the problem does not vary with time is known as static analysis. E$ample2 stress analysis on a beam Dynamic analysis2 The solution of the problem varies with time is known as dynamic analysis E$ample2 vibration analysis problem. !. Differentiate bet,een &lobal and loal aes. ocal a$es are established in an element. #ince it is in the element level, they change with the change in orientation of the element. The direction differs from element to element. 0lobal a$es are defined for the entire system. They are same in direction for all the elements even though the elements are differently oriented. $. Distin&#ish bet,een "otential ener&y f#ntion and "otential ener&y f#ntional f a system has finite number of degree of freedom 3/&,/',and /(!, then the potential energy e$pressed as, f 3/&,/',and /(! t is known as function. f a system has infinite degrees of freedom then the total potential energy is 4 5 6 7 3-8!. This is functional. '. What are the ty"es of loadin& atin& on the str#t#re? )ody force 3f!, Traction force 3T!, "oint load 3"! (. Define the body fore A body force is distributed force acting on every elemental volume of the body 6nit2 *orce per unit volume. E$ample2 #elf weight due to gravity ). Define tration fore Traction force is defined as distributed force acting on the surface of the body. 6nit2 *orce per unit area. E$ample2 *rictional resistance, viscous drag, surface shear *. What is "oint load? "oint load is force acting at a particular point which causes displacement. 1+. What are the basi ste"s in/ol/ed in the finite element modelin&. Discretiation of structure. %umbering of nodes. 11. Write do,n the &eneral finite element e7#ation.
{F }=[K ]{u} 12. What is disreti0ation? The art of subdividing a structure in to a convenient number of smaller components is known as discretiation. 13. What are the lassifiations of oordinates? 0lobal coordinates, ocal coordinate, %atural coordinate. 1!. What is 8lobal oordinates? The points in the entire structure are defined using coordinates system is known as global coordinate system. 1$. What is nat#ral oordinates? A natural coordinate system is used to define any point inside the element by a set of dimensionless number whose magnitude never e$ceeds unity. This system is very useful in assembling of stiffness matrices. 1'. Define sha"e f#ntion. Appro$imate relation 9 3$,y! 5 %& 3$,y! 9& 7 %' 3$,y! 9' 7 %( 3$,y! 9( here 9&, 9', and 9( are the values of the field variable at the nodes %&, %', and %( are the interpolation functions. %&, %', and %( are also called shape functions because they are used to e$press the geometry or shape of the element. 1(. What are the harateristi of sha"e f#ntion? t has unit value at one nodal point and ero value at other nodal points. The sum of shape function is e/ual to one. 1). Why "olynomials are &enerally #sed as sha"e f#ntion? Differentiation and inte&ration of "olynomial are 7#it easy. The accuracy of the result can be improved by increasing the order of the polynomial. t is easy to formulate and computerie the finite element e/uations 1*. 9o, do yo# al#late the si0e of the &lobal stiffness matri? 0lobal stiffness matri$ sie 5 %umber of nodes : Degrees of freedom per node. 2+. %tate the "ro"erties of stiffness matri It is a symmetri matri The sum of elements in any column must be e/ual to ero t is an unstable element. #o the determinant is e/ual to ero. 21. Write do,n the e"ression of stiffness matri for one dimensional bar element.
22. Write do,n the e"ression of stiffness matri for a tr#ss element.
23. Write do,n the e"ression of sha"e f#ntion N and dis"laement # for one dimensional bar element. 65 %&u&7%'u' %&5 &-: ; , %' 5 : ; 2!. Define total "otential ener&y. Total potential energy, 4 5 #train energy 36! 7 potential energy of the e$ternal forces 3! 2$. %tate the "rini"le of minim#m "otential ener&y. Among all the displacement e/uations that satisfied internal compatibility and the boundary condition those that also satisfy the e/uation of e/uilibrium make the potential energy a minimum is a stable system. 2'. Write do,n the finite element e7#ation for one dimensional t,o noded bar element.
2(. What is tr#ss? A truss is defined as a structure made up of several bars, riveted or welded together. 2). %tates the ass#m"tion are made ,hile findin& the fores in a tr#ss. All the members are pin jointed. The truss is loaded only at the joint The self weight of the members is neglected unless stated. 2*. %tate the "rini"les of /irt#al ener&y? A body is in e/uilibrium if the internal virtual work e/uals the e$ternal virtual work for the every kinematically admissible displacement field 3+. What is essential bo#ndary ondition? "rimary boundary condition or E)1 )oundary condition which in terms of field variable is known as "rimary boundary condition. 31. What is meant by Nat#ral bo#ndary onditions? #econdary boundary natural boundary conditions which are in the differential form of field variable is known as secondary boundary condition 32. 9o, do yo# define t,o dimensional elements? Two dimensional elements are define by three or more nodes in a two dimensional plane. The basic element useful for two dimensional analysis is the triangular element.
UNIT 3 CONTINUU5 -4-5-NT% 1. What is C%T element? Three noded triangular elements are known as 1#T. t has si$ unknown displacement degrees of freedom 3u&, v&, u', v', u(, v(!. The element is called 1#T because it has a constant strain throughout it. 2. What is 4%T element? #i$ noded triangular elements are known as #T. t has twelve unknown displacement degrees of freedom. The displacement function for the elements are /uadratic instead of linear as in the 1#T. 3. What is :%T element? Ten noded triangular elements are known as
[ B]T -Strain displacement [ D]-Stress strain matrix [ B]-Strain displacement matrix ). Write do,n the stress strain relationshi" matri for "lane stress and strain onditions.
*. What is aisymmetri element? =any three dimensional problem in engineering e$hibit symmetry about an a$is of rotation such type of problem are solved by special two dimensional element called the a$isymmetric element 1+. What are the onditions for a "roblem to be aisymmetri? The problem domain must be symmetric about the a$is of revolution All boundary condition must be symmetric about the a$is of revolution All loading condition must be symmetric about the a$is of revolution 11. 8i/e the stiffness matri e7#ation for an aisymmetri trian&#lar element.
Stiffness matrix [K ]=[ B ]T [ D ][ B ]2π Ra
UNIT ! I%OR5-TRIC -4-5-NT% 1. What is the "#r"ose of Iso"arametri element? t is difficult to represent the curved boundaries by straight edges finite elements. A large number of finite elements may be used to obtain reasonable resemblance between original body and the assemblage. 2. Write do,n the sha"e f#ntions for ! noded retan&#lar elements #sin& nat#ral oordinate system. N 1 =
1
(1−ε )(1−η )
N 2
= 1 (1+ε )(1−η )
4
N 3 =
1
4
(1 +ε )(1+η )
4
N 4 =
1
(1 −ε )(1 +η )
4
3. Write do,n ;aobian matri for ! noded 7#adrilateral elements. J J
J
J 11
12
J
22
21
!. Write do,n stiffnes matri e7#ation for ! noded iso"arametri 7#adrilateral elements.
[ ]=t ∫ ∫
Stiffness matrix K
1
1
∂ε ∂ [ B ] [ D ][ B ] J η T
−1 −1
$. Define s#"er "arametri element. f the number of nodes used for defining the geometry is more than of nodes used for defining the displacement is known as super parametric element '. Define s#b "arametri element. f the number of nodes used for defining the geometry is less than number of nodes used for defining the displacement is known as sub parametric element. (. What is meant by Iso"arametri element? f the number of nodes used for defining the geometry is same as number of nodes used for defining the displacement is known as soparametric element. ). Is beam element an Iso"arametri element? )eam element is not an soparametric element since the geometry and displacement are defined by different order interpretation functions. *. What is the differene bet,een nat#ral oordinate and sim"le nat#ral oordinate?
1+. 11. 12. 13. 1!.
1$.
& 5 &-$;l ' 5 $;l What is rea oordinates? & 5 A&;A ' 5 A';A ( 5 A(;A What is sim"le nat#ral oordinate? A simple natural coordinate is one whose value between -& and &. 8i/e eam"le for essential bo#ndary onditions. The geometry boundary condition are displacement, slope. 8i/e eam"le for non essential bo#ndary onditions. The natural boundary conditions are bending moment, shear force What is meant by de&rees of freedom? hen the force or reaction act at nodal point node is subjected to deformation. The deformation includes displacement rotation, and or strains. These are collectively known as degrees of freedom. What is :%T element? Ten noded triangular elements are known as
UNIT $
2. %tate the methods of sol#tion to ei&en /al#e "roblems. There are essentially three groups of methods of solution of eigen value problems. a! Determinent based methods b! Transformation based method c! >ector iteration based method 3. What is nonhomo&eneo#s form? hen the specified values of dependent variables are non-ero, the boundary condition said to be nonhomogeneous. !. What is homo&eneo#s form? hen the specified values of dependent variables is ero, the boundary condition are said to be homogeneous. $. Define initial /al#e "roblem. An initial value problem is one in which the dependent variable and possibly is derivatives are specified initially. '. Define bo#ndary /al#e "roblem. A differential e/uation is said to describe a boundary value problem if the dependent variable and its derivatives are re/uired to take specified values on the boundary. (. Name any fo#r <- soft,are>s. a! A%#?# b! %A#T+A% c! 1@#=@# d! %#A ). Define &o/ernin& e7#ation. The basic mathematical representation which relates the field variable with load.
