Svcet Autonomous Quiz: Finite Element Methods

The answer "All of the above" is correct because FEM (Finite Element Method) is a numerical technique used to solve problems related to heat transfer, temperature, and potential. FEM can be applied to analyze and simulate the behavior of these parameters in various engineering and scientific applications. Therefore, FEM operates on all of the mentioned parameters.

The number of displacement polynomials used for an element depends on the degrees of freedom. Degrees of freedom refer to the number of independent variables or parameters that can be varied in a system. In the context of structural analysis, degrees of freedom represent the number of possible translations and rotations that a structural element can undergo. The displacement polynomials are mathematical functions used to represent the displacement of the element in terms of these degrees of freedom. Therefore, the correct answer is degrees of freedom.

Polynomial functions are commonly used to approximate the behavior of a system or function. In the context of finite element analysis, nodal displacements are used as parameters to determine the polynomial function that best represents the behavior of the system. By considering the displacements at specific nodes, the polynomial function can accurately describe the deformation and behavior of the system. Therefore, nodal displacements are the appropriate parameter for choosing a polynomial function in this context.

The displacements at Fixed support are equal to 0.

Higher order elements are also known as complex elements because they have more than one node and more than two elements. These elements are used to model complex behaviors in circuits or systems, such as capacitance, inductance, and non-linear components. Unlike linear elements, which have a linear relationship between voltage and current, complex elements exhibit non-linear behavior and require more complex mathematical models for analysis and simulation. Therefore, the term "complex elements" accurately describes these higher order elements.

Finite Element Method (FEM) is a numerical technique used to approximate solutions to complex engineering problems. It is based on dividing the problem domain into smaller elements and solving them individually. However, FEM cannot produce exact results like analytical, logical, and theoretical methods. Analytical methods involve solving equations using mathematical formulas, logical methods use logical reasoning to solve problems, and theoretical methods are based on theoretical principles. FEM is an approximation method that introduces errors due to discretization and simplifications, making it unable to produce exact results like these other methods.

Heat transfer takes place due to a temperature difference (∆T) between two objects or regions. When there is a difference in temperature, heat energy flows from the hotter object/region to the colder one, resulting in heat transfer. This transfer can occur through various mechanisms such as conduction, convection, and radiation. However, ∆T is the driving force behind heat transfer, as it determines the direction and rate of heat flow.

An axis-symmetric element is a type of element that possesses symmetry around an axis. This means that the element can be rotated around the axis and still maintain its shape and properties. In the case of a 2D element, it is assumed that the element is infinitely thin in one dimension, and the axis of symmetry lies along the thickness direction. This allows for simplifications in analysis and calculations, as the problem can be reduced to a 2D plane. Therefore, the correct answer is 2D.

Polynomial functions can be chosen based on nodal displacements. Nodal displacements refer to the movement or displacement of the nodes in a system or structure. In the context of polynomial functions, nodal displacements are used to determine the shape and behavior of the function. By analyzing the displacements at specific nodes, one can choose a suitable polynomial function that accurately represents the desired behavior or pattern of the system. Therefore, nodal displacements serve as a parameter for selecting the appropriate polynomial function.

The correct answer is F=KT. In the FEM (Finite Element Method) equation for temperature element, F represents the temperature, K is the thermal conductivity, and T is the temperature gradient. This equation relates the temperature and thermal conductivity to the temperature gradient, indicating that the temperature is directly proportional to the product of thermal conductivity and temperature gradient.

A triangular plane stress element has 6 degrees of freedom because each node has 2 degrees of freedom (displacement in x and y directions) and there are 3 nodes in a triangular element. Therefore, the total degrees of freedom for a triangular plane stress element is 2 x 3 = 6.

The sum of all shape functions is equal to +1.

Convection is the correct answer because it refers to the heat transfer that occurs between a solid and a liquid. Convection involves the movement of heat through the bulk movement of the liquid molecules. This can happen through the process of convection currents, where warmer molecules rise and cooler molecules sink, creating a continuous flow of heat transfer. Conduction, on the other hand, refers to heat transfer within a solid or between solids in direct contact, while radiation is the transfer of heat through electromagnetic waves.

The given displacement function represents the displacement of a 1-D, two node linear element in terms of the shape function. The shape function N1 represents the displacement at node 1, and the shape function N2 represents the displacement at node 2. Therefore, the correct answer is u = N1u1 + N2u2, which means that the displacement of the element is a linear combination of the displacements at node 1 and node 2, weighted by the respective shape functions N1 and N2.

The given answer [B]T [D][B]2πrt is the correct explanation for the stiffness matrix for axisymmetric elements. The stiffness matrix represents the relationship between the applied forces and resulting displacements in a structure. In axisymmetric elements, the stiffness matrix is determined by the geometric properties of the element, such as the radius (r) and thickness (t), as well as the material properties represented by the matrix [D]. The transpose of the shape function matrix [B]T is multiplied by the material and geometric matrices to obtain the stiffness matrix. The inclusion of 2πrt in the answer indicates the contribution of the element's geometry to the stiffness.

Iso-parametric elements are irregular elements. These elements are used in finite element analysis to model complex geometries with curved boundaries. Unlike regular elements, which have straight sides, iso-parametric elements have curved sides that match the shape of the boundary. This allows for more accurate representation of the geometry and better approximation of the solution. Therefore, the correct answer is irregular.

The correct answer is "non-dimensional axis". The transformation axis refers to the axis that has been converted or scaled to a dimensionless or non-dimensional form. This term is commonly used in various fields such as mathematics, physics, and engineering, where dimensional analysis is performed to eliminate physical units and express quantities in terms of ratios or proportions. The non-dimensional axis allows for easier comparison and analysis of data without the need for specific units of measurement.

A six noded triangular element is known as a linear strain triangular element because it uses linear interpolation functions to approximate the strain within the element. This means that the element assumes a linear variation of strain across its shape, which simplifies the analysis and calculations involved. The linear strain triangular element is commonly used in finite element analysis for structural and mechanical engineering applications.

The finite element method is mostly used in the field of engineering mechanics because it is a numerical technique that allows for the analysis and simulation of complex mechanical systems. It is particularly useful in solving problems related to structural mechanics, such as determining the stress and strain distribution in a structure under different loading conditions. By dividing the structure into smaller elements and using mathematical models to describe their behavior, the finite element method provides a powerful tool for engineers to analyze and optimize the design of mechanical systems.

Subparametric refers to a situation where the number of nodal points used in a numerical analysis or simulation exceeds the number of geometry points. In other words, there are more computational points than actual physical points in the system being analyzed. This can be useful in certain situations where a higher level of accuracy or resolution is desired.