Finite-Element Analysis

What is the fundamental process of Finite-Element Analysis (FEA) when applied to a continuous elastic structure?

In the context of FEA, what are the fundamental governing entities of an element where it connects to other elements and where boundary conditions are assigned?

What are the two primary categories of errors that are considered inevitable in the finite-element method?

What is the primary cause of discretization errors in a finite-element model?

A linear truss element can be modeled as a simple linear spring. If the element has a cross-sectional area A, a length l, and an elastic modulus E, what is its spring rate, k?

In an analysis of an aluminum step-shaft, a section labeled AB has a cross-sectional area of 0.100 square inches, a length of 10 inches, and an elastic modulus E of 10 Mpsi (10,000,000 psi). What is the calculated spring rate, k1, for this section?

In the two-element spring system from Example 19-1, a force of 1000 lbf is applied at node 2, and node 3 is assumed to move to a gap of 0.002 in. The system is solved using the matrix equation 1000 = 10^5 * [-1(0) + 2.25*u2 - 1.25(0.002)]. What is the resulting displacement of node 2 (uB)?

What is the term for the network of elements and nodes used to discretize a region in a finite element model?

In FEA, what is the intended outcome of performing mesh refinement in an area with high stress gradients?

Which method of mesh generation requires the user to first divide the structure into well-defined regions, after which computer algorithms automatically mesh those specific regions?

What is the primary function of a 'rigid element' in a finite-element model?

According to Saint-Venant’s principle as it applies to FEA, if an analyst is not concerned about stresses near points of load application, how can the load be applied?

Which type of FEA element from the element library is described as a 'Pin-ended bar in tension or compression'?

Which of the following FEA analyses must be performed first to provide the necessary input for a thermal stress analysis?

In a vibration analysis of a component, what information does a modal analysis provide?

In a finite element buckling analysis, the software typically returns a load multiplier. What does this load multiplier represent?

When comparing FEA models for a step shaft, a simple five-element beam model is created. Where are nodes required in such a model?

In a modal analysis of a step beam, a 20-element beam model resulted in a first natural frequency of 322 Hz, while a 56,384-element solid model gave a frequency of 316 Hz. What is the approximate percentage difference between these two results?

An FEA solid model of a step shaft under a bending load predicts a maximum tensile stress of 23.9 kpsi at a fillet. An analytical calculation for the same location yields a stress of 25.03 kpsi. What is the relationship between the FEA result and the analytical prediction?

What is the single most difficult part of accurately modeling a structure for a finite-element analysis?

According to Table 19-1, what is the primary application of an 8-node hexagonal (brick) element?

Which of the following element types does NOT support rotational degrees of freedom, meaning concentrated moments cannot be directly applied to its nodes?

What is the consequence of having an abrupt mesh transition in an FEA model?

If the model length and force units in an FEA gravity loading analysis are inches and lbf, what value should be supplied for the gravity constant, g?

Who is credited with first using the expression 'finite element' in the context of plane stress analysis?

For a thin plate with a central hole subjected to thermal loading, where do the maximum compressive stresses occur?

In the context of FEA, what does the term 'element library' refer to?

When is it appropriate to use a simple beam-element model for a shaft analysis instead of a full solid model?

In Example 19-1, what is the stress in section AB of the aluminum step-shaft, which has a cross-sectional area of 0.100 square inches and an internal tensile force of 555.6 lbf?

What type of analysis is used to predict the critical load for a thin-walled structure, such as the aluminum beverage can shown in Figure 19-10?

In the automeshing example of the thin-plate model, the first mesh with 294 elements yielded a maximum von Mises stress of 4110.4 psi. A refined mesh with 1008 elements yielded a stress of 4184.9 psi. What does this small percentage increase suggest?

What is the result of a modal analysis mode shape calculation?

To model a pure moment on elements that do not support rotational degrees of freedom, like brick elements, how must the load be applied?

What is the recommended modeling approach when analyzing a shaft where the bearings are known to be something between simply supported and fixed?

What are the three categories of elements listed in the text, based on their geometric shape?

For the simply supported step shaft model in Figure 19-8, how was the boundary condition at the left end modeled for the solid elements?

What is the primary characteristic of the strain within a three-node, plane stress, simplex triangular element?

In the thermal analysis of a steel plate with a coefficient of thermal expansion of 6.5 x 10^-6 per degree F, what was the maximum von Mises stress found when the plate was heated from 0 F to a non-uniform final temperature distribution?

What happens to the system matrix once each element within a structure is defined locally in matrix form?

What type of analysis follows a modal analysis in order to see how a component's modes behave to dynamic input?

For the two-element spring system in Figure 19-4, what is the entry in the global stiffness matrix that corresponds to the interaction between node 1 and node 2?

In the comparison of vibration analysis for a step beam, the second free-vibration mode had a frequency of 1296 Hz for the beam model and 1249 Hz for the solid model. What is the approximate percentage difference between these two models for the second mode?

What does a 'Gap' element from the special-purpose element library typically model?

In a manual mesh generation process, what is a key risk that requires care when editing the input text file?

What is the primary advantage of using a higher-order element, such as an eight-node quadrilateral, over a simple three-node triangle?

What is the method called that uses the mode shapes from a modal analysis together with modal superposition to find the response of a structure to dynamic loading?

When comparing FEA modeling techniques for a shaft, the solid model deflection at a certain point was found to be -0.00981 in, while a three-element beam model gave a deflection of -0.00938 in. What is the approximate percentage difference of the solid model result compared to the beam model?

Why must an analyst be careful when reviewing stress results in the immediate vicinity of a single-node load application point?

What type of element is described in Table 19-1 as being used for modeling 'Axial, torsional, and bending' loads, with or without load stiffening?

After a finite-element solution is complete, and all unknown displacement degrees of freedom are determined, what is the next step to find the strains and stresses?