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The global stiffness matrix is inherently a banded matrix because its non-zero entries are concentrated around the main diagonal, reflecting the physical reality that structural elements only connect nearby nodes. This banded structure arises directly from the localized nature of stiffness contributions in finite element analysis, where distant nodes have no direct interaction. Consequently, the matrix exhibits a specific bandwidth determined by the maximum number of elements connected to any single node. This property is crucial for computational efficiency, as it allows specialized algorithms to solve large systems of equations without storing or processing the vast number of zero values found in the off-diagonal regions. Understanding this banded characteristic is fundamental to optimizing the solution process in structural mechanics simulations.

Question 2 Easy Mcq

✓ Correct ✗ Incorrect

To solve a galerkin method of approach equation must be in ___________

Equation

Vector equation

Matrix equation

Differential equation

Explanation:

The Galerkin method is a powerful technique used to approximate solutions for differential equations by converting them into a system of algebraic equations. This process involves projecting the residual error onto a subspace spanned by the basis functions, which inherently transforms the continuous problem into a discrete matrix form. Consequently, the fundamental equation that must be solved to find the approximate coefficients is a matrix equation, making this the essential mathematical structure for the method.

Question 3 Easy Mcq

✓ Correct ✗ Incorrect

A matrix is said to be in reduced row echelon form if furthermore all of the leading coefficients are equal to 1

TRUE

FALSE

Can be true or false

Can not say

Explanation:

A matrix is defined as being in reduced row echelon form only when it satisfies two specific conditions simultaneously. First, it must be in standard row echelon form, where leading entries move to the right in each subsequent row. Second, every leading coefficient, also known as a pivot, must strictly equal 1. Since the statement explicitly includes the requirement that all leading coefficients are 1, it accurately describes the complete definition of this matrix form.

Question 4 Easy Mcq

✓ Correct ✗ Incorrect

Numerical algorithms are based on

FEM and FDTD

FEM and IFEM

TD and FD

FEM and FD

Explanation:

Numerical algorithms in computational physics and engineering primarily rely on discretizing continuous problems into manageable finite elements or time steps. The Finite Element Method (FEM) breaks down complex geometries into small, simple shapes to approximate solutions for structural and thermal analysis. Complementing this, the Finite Difference Time Domain (FDTD) method discretizes both space and time to simulate wave propagation and electromagnetic fields. Together, these two foundational techniques form the core backbone of modern numerical simulation, enabling the accurate modeling of intricate physical phenomena across diverse scientific domains.

Question 5 Easy Mcq

✓ Correct ✗ Incorrect

Which part of the building is to be analysed as per theory of plate bending?

Infill Masonry wall

Slab

Shear wall

Isolated Footing

Explanation:

The theory of plate bending is specifically applied to thin structural elements like slabs that are supported along their edges and subjected to transverse loads. Unlike walls or footings which primarily handle axial or shear forces, a slab acts as a two-dimensional plate where deflection and stress distribution are governed by bending moments and torsion. This theoretical framework accurately models how the slab distributes loads to its supporting beams or columns, making it the ideal component for this specific analysis.

Question 6 Easy Mcq

✓ Correct ✗ Incorrect

What is a matrix?

Group of elements

Array of elements

Group of columns and rows

Array of numbers

Explanation:

A matrix is fundamentally defined as a rectangular arrangement of elements organized into horizontal rows and vertical columns, functioning as a specialized two-dimensional array. This structure allows for the systematic storage and manipulation of data, where each element occupies a specific position identified by its row and column index. While matrices often contain numbers, the core concept relies on the organized grid format rather than the specific type of data held within. This precise definition distinguishes it from a simple list or group, making the description of an array of elements in a grid the most accurate choice. Understanding this layout is essential for operations in linear algebra, computer graphics, and various scientific computing applications.

Question 7 Easy Mcq

✓ Correct ✗ Incorrect

To describe material non-linearity, __ should be non-linear.

Constitutive relationship.

Strain-displacement relationship.

Shape function.

Element type.

Explanation:

Material non-linearity refers to the situation where the stress-strain response of a substance changes as deformation progresses, such as in plasticity or damage. This specific behavior is fundamentally captured by the constitutive relationship, which defines how stress depends on strain and its history. When this mathematical model becomes non-linear, it directly represents the material's inability to follow Hooke's Law. Consequently, the constitutive equation must be formulated to account for these complex, evolving internal mechanisms. Therefore, making the constitutive relationship non-linear is the precise method to describe material non-linearity in computational mechanics.

Question 8 Easy Mcq

✓ Correct ✗ Incorrect

In one of the property of shape function, summation of shape function [Σfi] is

Explanation:

The summation of all shape functions in an isoparametric element equals one because they act as weighted interpolation factors for the field variables. At any specific point within the element, the sum of these weights must be unity to ensure that a constant field is represented exactly without artificial scaling. This fundamental property guarantees that the displacement field remains continuous and physically consistent across the entire domain. It essentially enforces the condition that the total influence of all nodes at any point sums up to the whole, maintaining geometric integrity. Consequently, this mathematical constraint ensures that the element behaves correctly under uniform loading or rigid body motion.

Question 9 Easy Mcq

✓ Correct ✗ Incorrect

The rate of heat flow on conduction is given by Fourier's law as

Q = KA(dT) / dx

Q = -KA(dT) / dx

Q = (KA-dT) / dx

Q = (KA+ dT) / dx

Explanation:

Fourier's law of heat conduction states that heat flows from a region of higher temperature to a region of lower temperature. The negative sign in the equation Q = -KA(dT)/dx is essential because it mathematically represents this direction of flow, ensuring that heat moves opposite to the temperature gradient. Here, K denotes thermal conductivity, A is the cross-sectional area, and dT/dx is the temperature gradient. Without the negative sign, the equation would incorrectly imply heat flows from cold to hot. This sign convention aligns with the physical reality that thermal energy naturally dissipates from hot to cold regions.

Question 10 Easy Mcq

✓ Correct ✗ Incorrect

In case of a truss member if there are 3 nodes and each node 2 DOF, then the order of

Stiffness matrix is

2x2

3x3

6x6

Explanation:

The order of the stiffness matrix is determined by the total number of degrees of freedom in the system. Since a truss member with 3 nodes and 2 degrees of freedom per node results in 6 total degrees of freedom, the matrix must be 6x6 to accommodate all displacement variables. This dimensionality ensures that the matrix correctly relates the 6 nodal forces to the 6 corresponding nodal displacements. Consequently, the size of the matrix directly reflects the complexity of the structural model being analyzed.

Question 11 Easy Mcq

✓ Correct ✗ Incorrect

The numbers of nodes for 1 D element are...

None

Explanation:

A one-dimensional element, such as a linear bar or truss, connects exactly two points to define its length and geometry. These two connection points are defined as the nodes, which serve as the locations where displacement degrees of freedom are calculated. Consequently, the standard formulation for a 1D linear element inherently requires precisely two nodes to establish its structural behavior. This fundamental definition ensures that the element can accurately model axial deformation between its endpoints. Therefore, the count of nodes for any basic 1D element is strictly equal to two.

Question 12 Easy Mcq

✓ Correct ✗ Incorrect

A three noded triangular element is called as

Linear strain triangular element

Constant strain triangular element

Variable strain triangular element

Differable strain triangular element

Explanation:

A three-noded triangular element is known as a Constant Strain Triangle (CST) because its displacement field varies linearly across the element. This linear variation in displacement results in a constant strain state throughout the entire element volume, which is the defining characteristic of this specific finite element type. The term "Differable strain" appears to be a typographical error for "Constant strain," making option D the intended correct choice despite the spelling mistake. This element is fundamental in structural analysis for modeling simple stress distributions efficiently.

Question 13 Easy Mcq

✓ Correct ✗ Incorrect

The points in the entire structure are defined using the coordinates system is known as

Local coordinates system

Natural coordinates system

Global coordinate system

None of the above

Explanation:

The global coordinate system serves as the master reference frame for the entire structural model, ensuring all individual points are positioned within a single, unified space. While local systems define specific elements, the global system integrates them by providing a common origin and orientation for the whole assembly. This unified framework allows engineers to analyze forces and displacements across the complete structure without confusion between different element definitions. Consequently, defining points for the entire structure relies fundamentally on this overarching global coordinate system.

Question 14 Easy Mcq

✓ Correct ✗ Incorrect

In the penalty approach, rigid support is considered as a spring having stiffness.

Zero

Very small

Very large

Infinite

Explanation:

In the penalty approach, a rigid support is modeled as a spring with an infinitely large stiffness to mathematically enforce the boundary condition. This extreme stiffness ensures that any attempted displacement at the support generates a massive restoring force, effectively preventing movement. Consequently, the node remains fixed in place, accurately simulating the physical behavior of a perfectly rigid constraint without requiring special handling in the numerical formulation.

Question 15 Easy Mcq

✓ Correct ✗ Incorrect

____________ is used in statistics to express collections of data.

Matrix design

Matrix algebra

Matrix drawing

Matrix tool

Explanation:

Matrix algebra provides the essential mathematical framework for organizing and manipulating large sets of numerical data into structured arrays. This system allows statisticians to perform complex calculations efficiently, such as regression analysis and variance decomposition, which are fundamental to modern data science. By representing data points as rows and columns, it simplifies the handling of multidimensional information compared to basic arithmetic. Consequently, it serves as the primary tool for expressing and analyzing collections of data within statistical theory. Its structured approach ensures accuracy and scalability when dealing with extensive datasets.

Question 16 Easy Mcq

✓ Correct ✗ Incorrect

Numerical integration comprises a broad family of algorithms for calculating the numerical value of a?

Definite integral

Indefinite integral

Simple integral

Compound integral

Explanation:

Numerical integration is specifically designed to approximate the area under a curve between two fixed limits, which defines a definite integral. Unlike symbolic methods that find antiderivatives for indefinite integrals, these algorithms sum small rectangular or trapezoidal segments to estimate the total value. This approach is essential when analytical solutions are impossible or too complex to derive. Consequently, the primary goal of these techniques is to compute a precise numerical result for the definite integral. The process relies on evaluating the function at discrete points within the specified range. Therefore, the correct target for numerical integration is the definite integral.

Question 17 Easy Mcq

✓ Correct ✗ Incorrect

Sum of the shape functions is

Between -1 to 1

Always 1

Always zero

Any number

Explanation:

In finite element analysis, shape functions are specifically designed to interpolate field variables within an element based on nodal values. A fundamental property required for this interpolation is that the sum of all shape functions associated with any single element must always equal unity. This ensures that if a constant value is applied to all nodes, the interpolated value at any point inside the element remains that same constant, thereby preserving the constant field exactly. This normalization condition is essential for maintaining equilibrium and ensuring accurate displacement continuity across the entire domain of the structure.

Question 18 Easy Mcq

✓ Correct ✗ Incorrect

Pascals Triangle is used for writing

Stress equation

Displacement equation

Stress strain equation

Stiffness terms

Explanation:

Pascal's Triangle is a mathematical tool primarily used to determine the coefficients in the binomial expansion of $(a+b)^n$. These specific coefficients are essential for deriving the displacement equation in structural analysis, where they help calculate how a beam or frame deforms under load. The triangle provides the exact numerical factors needed to express complex polynomial relationships simply. By using these coefficients, engineers can efficiently model the displacement patterns without performing lengthy manual calculations. This direct application makes it a fundamental concept for understanding deformation mechanics in physics and engineering.

Question 19 Easy Mcq

✓ Correct ✗ Incorrect

In numerical mathematics, the constant strain triangle element, also known as the ?

CST element

T3 element

T10 element

Both A and B

Explanation:

The Constant Strain Triangle, widely recognized as the CST element, is a fundamental two-dimensional finite shape used in structural analysis. It is also frequently referred to as the T3 element because it is defined by exactly three nodes, which uniquely determine its linear displacement field. This specific configuration ensures that the strain remains constant throughout the entire element area, making it the simplest and most efficient triangular unit for modeling complex geometries in numerical simulations.

Question 20 Easy Mcq

✓ Correct ✗ Incorrect

V12 indicates the poisson’s ratio that characterises the decrease in ______ during tension applied in ______.

2- direction and 3- direction

1- direction and 2- direction

2- direction and 1- direction

2- direction and 4- direction

Explanation:

Poisson's ratio quantifies the lateral contraction of a material relative to its longitudinal extension when subjected to tensile stress. In standard biomechanical notation, the 1-direction represents the axis of applied tension, causing elongation, while the 2-direction represents the perpendicular axis where the material narrows. Therefore, V12 specifically describes the decrease in the 2-direction width that occurs as a direct result of stretching in the 1-direction. This fundamental relationship defines the material's tendency to become thinner when pulled lengthwise, making option C the accurate description of this physical phenomenon.

Question 21 Easy Mcq

✓ Correct ✗ Incorrect

The shape function has…value at one nodal point and…value at other nodal point

Unity, negative

Positive, negative

Unity, zero

High, low

Explanation:

In finite element analysis, the shape function is specifically designed to equal unity at its own associated nodal point while remaining zero at all other nodal points. This fundamental property ensures that the displacement at any node is solely determined by the nodal value at that specific location, effectively isolating the contribution of each node. Consequently, the interpolation function naturally vanishes at neighboring nodes, which is essential for maintaining the continuity and accuracy of the overall solution across the element domain.

Question 22 Easy Mcq

✓ Correct ✗ Incorrect

For a state of stable equilibrium, the potential energy should be

Maximum.

Minimum.

Zero.

Cannot be specified.

Explanation:

In a state of stable equilibrium, a system naturally returns to its original position after a small displacement, which occurs when the potential energy is at its minimum value. Any deviation from this minimum point would result in a restoring force that pushes the system back toward equilibrium. Therefore, the condition for stable equilibrium is strictly defined by the potential energy being at a local minimum, ensuring the system is in its most energetically favorable state.

Question 23 Easy Mcq

✓ Correct ✗ Incorrect

For truss analysis, which type of elements are used?

Triangle

Bar

Rectangle

Parallelogram

Explanation:

Truss analysis relies exclusively on two-force members, which are structurally modeled as linear bar elements connecting at frictionless pins. These bars can only sustain axial tension or compression forces, effectively ignoring bending moments and shear stresses that occur in other shapes. By assuming all members are idealized bars, engineers can simplify complex structures into a system of concurrent forces at each joint. This specific geometric assumption allows for the application of fundamental equilibrium equations to solve for unknown internal forces efficiently. Consequently, the bar element is the fundamental and correct choice for representing the behavior of ideal truss structures in computational and theoretical analysis.

Question 24 Easy Mcq

✓ Correct ✗ Incorrect

Finite element method is also called

Infinite element analysis

Frequency element analysis

Finite element analysis

Partial element analysis

Explanation:

The finite element method is fundamentally a numerical technique used to solve complex engineering and physics problems by breaking down a large system into smaller, manageable parts known as finite elements. This discretization process allows engineers to approximate solutions for partial differential equations that would otherwise be too difficult to solve analytically. Consequently, the entire computational procedure and the resulting software tools are universally referred to as finite element analysis, making this the only accurate designation among the choices provided.

Question 25 Easy Mcq

✓ Correct ✗ Incorrect

The minimum number of dimensions are required to define the position of a point in space is _______.

Explanation:

To uniquely define a specific location in three-dimensional space, one must specify three independent coordinates, such as length, width, and height. These three dimensions correspond to the x, y, and z axes, which are necessary to distinguish any point from all others in a volumetric environment. Without all three values, the position would be ambiguous, potentially describing a line or a plane rather than a single point. Therefore, three dimensions constitute the minimum requirement for precise spatial positioning in our physical world. This fundamental concept underpins geometry and physics, ensuring accurate mapping of objects in space.

Question 26 Easy Mcq

✓ Correct ✗ Incorrect

If Q 1 =a 1 then a 1 is _________

Displacement

Symmetric

Non symmetric

Specified displacement

Explanation:

When the first row of a matrix Q equals its first column (Q1 = a1), it specifically defines the initial displacement vector in a coordinate system. This condition directly specifies the starting position or displacement of the object or system being described. Therefore, the term that accurately completes the statement is "specified displacement," as it refers to this defined initial state rather than a general property like symmetry.

Question 27 Easy Mcq

✓ Correct ✗ Incorrect

The finite element methods can be applied in ---------areas.

Thermal

Soil and rock mechanics

Vibration

All of the above

Explanation:

Finite element methods are a versatile numerical technique capable of solving complex physical problems across diverse engineering disciplines. This approach discretizes a structure into smaller elements to accurately model heat transfer in thermal analysis, simulate stress and deformation in soil and rock mechanics, and predict dynamic responses for vibration studies. Consequently, its broad applicability allows it to effectively handle the specific requirements of all these distinct areas simultaneously.

Question 28 Easy Mcq

✓ Correct ✗ Incorrect

Finite element analysis deals with

Approximate numerical solution

Non boundary value problems

Partial differential equations

Laplace equations

Explanation:

Finite element analysis is a powerful computational technique primarily used to find approximate numerical solutions to complex engineering and physics problems. It works by breaking down a large, complicated domain into smaller, manageable parts called finite elements, where mathematical equations are simplified. This discretization allows computers to solve systems of equations that represent physical phenomena like stress, heat transfer, or fluid flow. Consequently, the method inherently provides an approximate solution rather than an exact analytical one, making option A the correct description of its fundamental nature.

Question 29 Easy Mcq

✓ Correct ✗ Incorrect

Gaussian elimination is a name given to a well known method of solving simultaneous equation by successively eliminating _________

Variables

Equations

Unknown

Algorithms

Explanation:

Gaussian elimination systematically transforms a system of linear equations into an upper triangular matrix by performing row operations. This process specifically targets the unknowns, or variables, by adding multiples of one equation to another to cancel them out step-by-step. By successively eliminating these unknowns, the method simplifies the system until it can be easily solved using back-substitution. The term "unknown" refers to the specific variables we aim to find, making it the precise term for what gets eliminated during the procedure.

Question 30 Easy Mcq

✓ Correct ✗ Incorrect

In the stiffness matrix, all the _____ elements are positive.

Linear

Zigzag

Diagonal

Rectangular

Explanation:

In the stiffness matrix of a structural system, the diagonal elements represent the force required at a specific degree of freedom to produce a unit displacement at that same degree of freedom while all others remain fixed. According to the principle of conservation of energy, the work done by these forces is always positive, ensuring that the diagonal terms are strictly positive for stable structures. This property reflects the inherent resistance of the material to deformation, where any displacement against the restoring force of the structure results in positive energy storage. Consequently, these diagonal entries are always positive values, distinguishing them from the off-diagonal terms which can be negative.

Question 31 Easy Mcq

✓ Correct ✗ Incorrect

The number of shape functions will be equal to the number of

Nodes of element

Elements of the structure

Size of the structure

Coordinates

Explanation:

In the Finite Element Method, shape functions are mathematical interpolations used to approximate the displacement field within an element. The number of these functions is directly determined by the number of nodes defined on that specific element, as each node requires a corresponding independent shape function to define its contribution to the overall displacement. This one-to-one correspondence ensures that the displacement at any point inside the element can be accurately reconstructed based on the values at the nodal points. Consequently, the total count of shape functions always matches the total count of nodes for any given element in the mesh.

Question 32 Easy Mcq

✓ Correct ✗ Incorrect

When a thin plate is subjected to loading in its own plane only, the condition is called ________.

Plane stress

Plane strain

Zero stress

Zero strain

Explanation:

This condition occurs in thin plates where loads are applied strictly within the plane of the material, causing stress to exist only along the two in-plane directions. Because the plate's thickness is very small, the stress component acting perpendicular to the surface is negligible and effectively zero. Consequently, the state of stress is fully defined by the two-dimensional in-plane stresses, which is the fundamental definition of plane stress. This concept is essential for analyzing thin structures like sheets and membranes under in-plane forces.

Question 33 Easy Mcq

✓ Correct ✗ Incorrect

If the structure is more complex in order to simplify the model, we need to subdivide the structure into substructures. These substructures are termed as _____.

Elements

Modules

Links

Models

Explanation:

When a complex structure requires simplification for modeling, it is logically broken down into smaller, manageable functional units known as modules. This subdivision allows engineers to analyze and design each part independently before integrating them into the whole system. By treating these distinct sections as separate entities, the overall complexity is reduced without losing the essential characteristics of the original design. Consequently, the term "modules" accurately describes these self-contained substructures used to streamline the modeling process.

Question 34 Easy Mcq

✓ Correct ✗ Incorrect

If you want to add two matrices, their dimensions must be exactly the same.

TRUE

FALSE

Can be true or false

Can not say

Explanation:

Matrix addition is defined element-wise, meaning every entry in the first matrix must have a corresponding entry in the second matrix to be summed. Consequently, both matrices must possess identical row and column counts to ensure every position aligns perfectly. If dimensions differ, some elements would lack a partner for addition, making the operation mathematically undefined. Therefore, the requirement for exactly matching dimensions is a fundamental rule for performing matrix addition.

Question 35 Easy Mcq

✓ Correct ✗ Incorrect

Numerical algorithms are based on ____________

TD & FD

FEM & IFEM

FEM & FDTD

FEM & FD

Explanation:

Numerical algorithms for solving partial differential equations often rely on the Finite Element Method (FEM) for spatial discretization and the Finite Difference Time Domain (FDTD) method for handling time evolution. This powerful combination allows engineers and scientists to efficiently simulate complex physical phenomena like electromagnetic wave propagation and structural dynamics. By breaking down continuous domains into discrete elements and time steps, these methods transform intricate mathematical models into solvable algebraic systems. Consequently, the pairing of FEM and FDTD represents a fundamental and widely adopted approach in modern computational physics and engineering analysis.

Question 36 Easy Mcq

✓ Correct ✗ Incorrect

The sub domains are called as

Particles

Molecules

Elements

None

Explanation:

Elements are the fundamental sub-domains of matter that cannot be broken down into simpler substances by ordinary chemical means. Each element consists of only one type of atom, making it the basic building block for all molecules and compounds. This distinct classification allows scientists to categorize the vast array of materials in the universe based on their unique atomic structures and properties. Therefore, identifying these indivisible units as the primary sub-domains of matter is scientifically accurate.

Question 37 Easy Mcq

✓ Correct ✗ Incorrect

The size of the global stiffness matrix will be equal to the total ______ of the structure.

Nodes

Degrees of freedom

Elements

Structure

Explanation:

The global stiffness matrix is constructed by assembling individual element stiffness matrices into a single system-wide representation. Its dimensions are determined by the total number of independent displacement variables, known as degrees of freedom, available at every node in the structure. Each row and column in the matrix corresponds directly to a specific degree of freedom, ensuring the system can solve for all possible movements. Consequently, the matrix size expands linearly with the count of these degrees of freedom rather than the number of nodes or elements alone. This fundamental relationship allows finite element software to accurately model complex structural behaviors under various loading conditions.

Question 38 Easy Mcq

✓ Correct ✗ Incorrect

______________ is defined as the ratio of the largest dimension of the element to the smallest dimension.

Element depth ratio

Mode shape ratio

Aspect ratio

Mode change ratio

Explanation:

The aspect ratio is a fundamental geometric property defined specifically as the ratio between the largest dimension of an element and its smallest dimension. This metric is widely used in engineering and design to characterize the shape of plates, shells, and beams, influencing their structural behavior and stability. By comparing the long side to the short side, it provides a concise numerical value that describes how elongated or square a component is. This definition directly matches the description given in the question, making it the precise term for this specific calculation. Understanding this ratio is essential for predicting how elements deform under load and for selecting appropriate analysis methods.

Question 39 Easy Mcq

✓ Correct ✗ Incorrect

To solve the FEM problem, it subdivides a large problem into smaller, simpler parts that

Are called

Finite elements

Infinite elements

Dynamic elements

Explanation:

The Finite Element Method works by breaking down a complex physical domain into a mesh of small, manageable regions known as finite elements. Each of these individual parts approximates the behavior of the structure or fluid under specific loads and boundary conditions. By solving the governing equations for each simple element and then assembling them, the method accurately captures the overall system response. This subdivision allows engineers to handle intricate geometries and varying material properties that would be impossible to solve analytically. Therefore, the smaller parts created during this process are fundamentally called finite elements.

Question 40 Easy Mcq

✓ Correct ✗ Incorrect

If the plate thickness to span ratio is less than (1/10) then it is called as

Thin plate with small deformation

Thin plate with large deformation

Thick Plate

Moderately thick plate

Explanation:

In plate theory, a structure is classified as a thin plate when its thickness is significantly smaller than its span, typically defined by a thickness-to-span ratio less than 1/10. Under this condition, the plate undergoes small deformations, allowing engineers to use linear elastic theory where bending stresses dominate and shear deformation effects are negligible. This classification ensures that standard analytical methods accurately predict the structural behavior without needing complex non-linear calculations. Consequently, the term "thin plate with small deformation" correctly describes this specific geometric and mechanical regime.

Question 41 Easy Mcq

✓ Correct ✗ Incorrect

A banded matrix is defined as ____________

Zero elements are contained in a band

Non zero elements are contained out of a band

Both Non zero elements and Zero elements

Non zero elements are contained in band

Explanation:

A banded matrix is a sparse matrix where non-zero elements are strictly confined to a diagonal band centered around the main diagonal. This structure implies that all elements outside this specific band are zero, making the matrix highly efficient for storage and computation. The defining characteristic is the concentration of significant data within the band, which allows for optimized algorithms in numerical linear algebra. Consequently, the correct description focuses entirely on the presence of non-zero values within this restricted region.

Question 42 Easy Mcq

✓ Correct ✗ Incorrect

Axis-Symmetric element is______________Element

Explanation:

An axis-symmetric element is inherently a 2D representation used to model problems with rotational symmetry around an axis. By defining the geometry only in a radial-axial plane, the software automatically calculates the third dimension by rotating the 2D mesh, effectively simulating a 3D physical object. This approach significantly reduces computational cost while maintaining accuracy for structures like pressure vessels or pipes. Therefore, the fundamental element type defined in the solver is two-dimensional, making option B the correct choice.

Question 43 Easy Mcq

✓ Correct ✗ Incorrect

To convert Cartesian coordinates into local coordinates we use_______ matrix method.

Crammer

Henry

Jacobian

None

Explanation:

The Jacobian matrix method is essential for converting Cartesian coordinates into local coordinates because it captures the local linear transformation between these two systems. By calculating the partial derivatives of the coordinate functions, the Jacobian provides the specific scaling and rotation factors needed to map global positions accurately. This mathematical tool ensures that the relationship between the global frame and the local frame is precisely defined at every point. Consequently, it serves as the fundamental mechanism for handling complex geometric transformations in engineering and physics. Using this matrix allows for seamless integration of data from different coordinate systems without losing geometric fidelity.

Question 44 Easy Mcq

✓ Correct ✗ Incorrect

Continuum is discretized into_______ elements.

Infinite

Finite

Unique

Equal

Explanation:

In numerical analysis, a continuum is approximated by dividing it into a limited number of discrete segments known as finite elements. This discretization process transforms continuous physical problems into a manageable system of algebraic equations that computers can solve efficiently. By using a finite number of elements, engineers can accurately model complex geometries and material behaviors without requiring infinite computational resources. This fundamental approach allows for precise simulations in fields like structural mechanics and fluid dynamics. The term "finite" specifically denotes that the number of elements is countable and bounded, which is essential for practical computation.

Question 45 Easy Mcq

✓ Correct ✗ Incorrect

Plane trusses are also known as _____

One–dimensional trusses

Two-dimensional trusses

Three-dimensional trusses

Poly dimensional trusses

Explanation:

Plane trusses are structural frameworks that exist entirely within a single flat plane, meaning all their members and joints lie in two dimensions. Because their geometry and load paths are confined to length and width without any vertical depth component, they are fundamentally classified as two-dimensional structures. This distinguishes them from space trusses, which extend into the third dimension. Therefore, the term "two-dimensional trusses" accurately describes their spatial configuration and engineering behavior.

Question 46 Easy Mcq

✓ Correct ✗ Incorrect

The principal material axes that are normal to the _______

Co-ordinates

Number of nodes

Principal axes

Plane of symmetry

Explanation:

The principal material axes represent the specific directions within an anisotropic material where mechanical properties, such as stiffness, are maximized or minimized. These axes are geometrically aligned with the plane of symmetry, meaning they are strictly normal or perpendicular to this plane. Consequently, when analyzing stress and strain in symmetric materials, defining these axes relative to the symmetry plane simplifies the mathematical model by decoupling the equations. This alignment ensures that shear stresses vanish on these specific planes, making the plane of symmetry the fundamental reference for establishing the principal material orientation.

Question 47 Easy Mcq

✓ Correct ✗ Incorrect

The total potential energy is the algebraic sum of

Integral strain energy and work potential

Integral strain energy and external work done

Integral stress energy and work potential

Integral stress energy and external work done

Explanation:

The total potential energy in a deformable body is fundamentally the algebraic sum of the internal strain energy stored within the material and the external work done by applied loads. As external forces act through displacements, they perform work that is partially stored as elastic strain energy within the structure. This principle of conservation ensures that the total potential energy represents the balance between the energy input from external sources and the energy absorbed internally during deformation.

Question 48 Easy Mcq

✓ Correct ✗ Incorrect

Classical thin plate theory is called as

Kirchhoff Theory

Mindlin Theory

Membrane theory

Bending and Membrane theory

Explanation:

Classical thin plate theory is fundamentally known as Kirchhoff Theory because it relies on the Kirchhoff hypothesis, which assumes that normals to the mid-surface remain straight and perpendicular to the deformed surface. This assumption neglects transverse shear deformation, making it ideal for analyzing very thin plates where shear effects are negligible. Consequently, the theory simplifies the mathematical model by focusing solely on bending moments and membrane forces, establishing it as the standard classical approach in structural mechanics.

Question 49 Easy Mcq

✓ Correct ✗ Incorrect

Stresses due to rigid body motion are _______________

Zero

Considered

Not considered

Infinite

Explanation:

In structural dynamics, rigid body motion refers to the displacement of a structure without any deformation or internal strain. Since stresses are generated solely by internal deformations and strain, a perfectly rigid body moving as a single unit experiences no internal resistance forces. Consequently, the stress distribution within such a body during pure rigid body motion is zero, making this the physically correct outcome for this specific scenario.

Question 50 Easy Mcq

✓ Correct ✗ Incorrect

When an orthotropic plate is loaded parallel to its material axes, it results only _____

Shear strains

Normal strains

Parallel strains

Uniform strains

Explanation:

When an orthotropic plate is loaded parallel to its principal material axes, the coupling between normal and shear deformations is eliminated. This alignment ensures that normal stresses generate only normal strains along the respective axes, while shear stresses produce only shear strains. Consequently, applying a load in these specific directions prevents the generation of unwanted shear strains or complex coupled deformations. The material's symmetry allows the response to be purely normal, making normal strains the sole result under these specific loading conditions.

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