Unit-I FUNDEMENTAL CONCEPTS
State the methods of Engineering analysis
There are three methods of Engineering analysis. They are
1.Experimental methods 2.Analytical methods 3.Numerical methods or approximate methods
What is ment by finite element?
A small unit having definite shape of geometry and nodes is called finite element
What is ment by finite element analysis?
Finite element method is a numerical method for solving problems of engineering and mathematical physics.
Give Examples for the finite element
1.One dimensional elements (a)Truss elements (b)Bar, Beam elements 2.Two dimensional elements (a)Triangular elements (b)Rectangular elements 3.Three dimensional elements (a)Tetrahedral elements (b)Hexahedral elements
What is ment by node or joint
Each kind of finite element has a specific structural shape and is interconnected with the adjacent elements by nodal points or nodes. At the nodes, degrees of freedom are located. The forces will act only at nodes and not at any other place in the element.
What is the basis of finite element method
Discretization is the basis of finite element method. The art of subdividing a structure into a convenient number of smaller components is known as discretization
What are the types of boundary conditions
There are two types of boundary conditions. They are 1.Primary boundary condition 2.Secondary boundary condition
State the three phases of finite element method
The three phases are 1.Preprocessing 2.Analysis 3.Postprocessing
What is structural and non structural problems
Structural problems: In structural problems, displacement at each nodal point is obtained By using these displacement solutions, stress and strain in each element can be calculated. Non Structural problems: In non-structural problems, temperatures or fluid pressure at each nodal point is obtained By using these values, properties such as heat flow, fluid flow, etc., for each element can be calculated.
What are the methods are generally associated with the finite element analysis
The following two methods are generally associated with the finite element analysis. They are: 1.Force method 2.Displacement or stiffness method
Explain force method and stiffness method
In force method, internal forces are considered as the unknowns of the problem. In displacement or stiffness method, displacements of the nodes are considered as the unknowns of the problem. Amont them two approaches, displacement method is desirable.
Why polynomial type of interpolation functions are mostly used in FEM
The polunomial type of interpolation function are mostly used due to the following reasons:
1.Is is easy to formulate and computerize the finite element equations. 2. Is is easy to perform differentiation or integration 3. The accuracy of the results can be improved by increasing the order of the polynomial.
Name the variational methods
1. Ritz method 2. Rayleigh-Ritz method
Name the weighted residual methods
1. Point collocation method 2. Subdomain collocation method 3. Least squares method 4. Galerkins method
What is ment by post processing
Analysis and evaluation of the solution results is refered to as post processing. Post processor computer programs help the user to interpret the results by displaying them in graphical form.
What is Rayleigh-Ritz method
Rayleigh-Ritz method is a integral approach method which is useful for solving complex structural problems, encountered in finite element analysis. This method is possible only if a suitable functional is avaliable
What is ment by discretization and assemblage
The art of subdividing a structure into a convenient number of smaller components is known as discretization. These smaller components are then put together. The process of uniting the various elements together is called assemblage
What is ment by degrees of freedom
When the force or reaction act at nodal point, node is subjected to deformation. The deformation includes displacements, rotations, and/or strains. These are collectively known as degrees of freedom.
What is Aspect ratio
Aspect ratio is defined as the ration of the largest dimentsion of the element to the smallest diemension. In many cases, as the aspect ratio increases, the in accuracy of the solution increases. The conclusion of many researches is that the aspect ratio should be close to unity as possible.
What is truss element
The truss elements are the part of a truss structure linked together by point joints, which transmit only axial force to the element.
List the two advantages of post-processing
1. Required result can be obtained in graphical form 2. Contour diagrams can be used to understand the solution easily and quickly
If a displacement field in x direction is given u=2x2+4y2+6xy. Determine the strain in x direction
Ans: u=2x2+4y2+6xy Strain, e = u/x = 4x+6y
What are h and p versions of finite element method
h versions and p versions are used to improve the accuracy of the finite element method. In h versions, the order of polynomial approximation for all elements is kept constant and the number of elements are increased. In p version, the number of elements are maintained constant and the order of polynomial approximation of element is increased.
During discretization, mention the places where it is necessary to place a node
The following places are necessary to place a node during discretization process 1. Concentrated load acting point 2. Cross-section changing point 3. Different material interjunction point 4. Sudden change in load point
What is the difference between static and dynamic analysis
Static analysis: The solution of the problem does not vary with time is known as static analysis. Example: Stress analysis on a beam Dynamic analysis: The solution of the problem varies with time is known as dynamic analysis. Example: Vibration analysis problems.
Name any four FEA software
1. ANSYS 2. NASTRAN 3. COSMOS 4. NISA
Differentiate between global and local axes
Local axes are established in an element. Since it is the element level, they change with the change in orientation of the element. The direction differes from element to element. Global axes are defined for the entire system. They are same in direction for all the elements event houth the elements are differently oriented.
Distinguish between potential energy function and potential energy functional.
If a system has finite number of degrees of freedom(q1,q2 and q3), then the potential energy is expressed as, = f(q1,q2 and q3) It is known as function. If a system has infinite degrees of freedom, then the potential energy is expressed as, =(x,y, dy/dx , d2y/dx2, )dx
It is known as functional.
