MME 3360B Midterm Flashcards – University of Western Ontario – Study Guide
and Exam Review
State the objective of discretization of continuum - ✔✔to simultaneously find results at many
point of model, with numerical efficiency and versatility; to minimize disc errors
State major assumptions in the design of a finite element analysis - ✔✔linear (Hookes law),
small displacements that do not change structure stiffness; stress proportional to strain for
material
How are FEA equations formulated? - ✔✔Using polynomial functions related to the size and
shape of each finite element
What is the primary unknown in FEA: - ✔✔nodal displacements and nodal temperatures
(calculated first)
What is the nodal Degree of Freedom (D.O.F.)? - ✔✔nodal displacements or temperatures, E
Relation between total number of D.O.F and total number of nodes in the FEA model - ✔✔x, y
and z displacements are the three degrees of freedom for each node
What is the price to pay for replacing continuum with a set of finite elements?: -
✔✔discetization error: solution error or convergence error, and accuracy
What is a shape function - ✔✔A function of nodal displacements at any point in element(face,
edge, volume). In the 1st order element the shape function is a linear combination of nodal
displacement, in the2nd order element this a second order function
,What is the difference between h-element and p-element - ✔✔h: order doesn‟t change during
solution; characteristic element size (h)
p: order upgraded during solutions until acceptable solution; polynomial function of
displacement field
-h and p convergence: adding degrees of freedom to model for both
-h convergence: mesh refinement, element size h is modified (reduced)
-p convergence: increasing element order, mesh remains unchanged
What is a distorted element? What are types of element distortion - ✔✔Element after
mapping: aspect
ratio, skew, taper, curvature, mid-size node position, warpage
What is the difference between 1st and 2nd order element? - ✔✔1st order(draft quality):
Linear displacement
distribution, constant stress distribution; 2nd order(high quality): 2nd order displacement
distribution, linear
stress distribution
How do elements "communicate" between each other? - ✔✔though the nodal connections;
the model
stress is continuously distributed over the elements
List major steps in FEA and associated errors - ✔✔Create math model(modeling errors), FEA
model/
Discretization (discretization errors), Convergence(convergence errors), Results(solution error)
Sort in the order of calculation - ✔✔displacement, strain, stress
, What is the accuracy of FEA results? - ✔✔Combo of all errors
What are "artificial" restraints - ✔✔a restraint that is used to cause the model to act a certain
way as desired from the design of the mathemati-cal model, though the restraint may not exist
in reality; ex. soft springs, artificial stiffness (caused by discretization)
What is the objective of convergence analysis - ✔✔To observe how the data of interest
changes due to changes in choice of mesh; ideally the model should not be highly dependent on
mesh choice
What is an h convergence, why is it called h-convergence - ✔✔mesh refinement to add D.O.F.,
element size h is modified (reduced) globally or locally(mesh controls); named from element
characteristion dimension „h‟ which changes with each iteration
What are criteria of convergence analysis - ✔✔Conditions that must be satisfied for the
convergence process to stop; used for h/p-adaptive solution studies; results: less than 1%
difference
What is the p-convergence, why is it called p-convergence - ✔✔increasing element order with
each iteration until acceptable solution found, mesh element size unaffected; named from p-
order of polynomial function of displacement field
What is calculated in modal analysis - ✔✔-Frequency(natural/resonant) and associated
modes(shapes) of vibration; -can NOT calculate absolute displacement or stresses, only relative
displacementWhat is calculated in linear buckling analysis?
What is calculated in linear buckling analysis? - ✔✔Buckling load factor, buckling mode(shape),
Negative buckling load factor(reverse load and multiply by factor for buckling); -can NOT
calculate displacement
and Exam Review
State the objective of discretization of continuum - ✔✔to simultaneously find results at many
point of model, with numerical efficiency and versatility; to minimize disc errors
State major assumptions in the design of a finite element analysis - ✔✔linear (Hookes law),
small displacements that do not change structure stiffness; stress proportional to strain for
material
How are FEA equations formulated? - ✔✔Using polynomial functions related to the size and
shape of each finite element
What is the primary unknown in FEA: - ✔✔nodal displacements and nodal temperatures
(calculated first)
What is the nodal Degree of Freedom (D.O.F.)? - ✔✔nodal displacements or temperatures, E
Relation between total number of D.O.F and total number of nodes in the FEA model - ✔✔x, y
and z displacements are the three degrees of freedom for each node
What is the price to pay for replacing continuum with a set of finite elements?: -
✔✔discetization error: solution error or convergence error, and accuracy
What is a shape function - ✔✔A function of nodal displacements at any point in element(face,
edge, volume). In the 1st order element the shape function is a linear combination of nodal
displacement, in the2nd order element this a second order function
,What is the difference between h-element and p-element - ✔✔h: order doesn‟t change during
solution; characteristic element size (h)
p: order upgraded during solutions until acceptable solution; polynomial function of
displacement field
-h and p convergence: adding degrees of freedom to model for both
-h convergence: mesh refinement, element size h is modified (reduced)
-p convergence: increasing element order, mesh remains unchanged
What is a distorted element? What are types of element distortion - ✔✔Element after
mapping: aspect
ratio, skew, taper, curvature, mid-size node position, warpage
What is the difference between 1st and 2nd order element? - ✔✔1st order(draft quality):
Linear displacement
distribution, constant stress distribution; 2nd order(high quality): 2nd order displacement
distribution, linear
stress distribution
How do elements "communicate" between each other? - ✔✔though the nodal connections;
the model
stress is continuously distributed over the elements
List major steps in FEA and associated errors - ✔✔Create math model(modeling errors), FEA
model/
Discretization (discretization errors), Convergence(convergence errors), Results(solution error)
Sort in the order of calculation - ✔✔displacement, strain, stress
, What is the accuracy of FEA results? - ✔✔Combo of all errors
What are "artificial" restraints - ✔✔a restraint that is used to cause the model to act a certain
way as desired from the design of the mathemati-cal model, though the restraint may not exist
in reality; ex. soft springs, artificial stiffness (caused by discretization)
What is the objective of convergence analysis - ✔✔To observe how the data of interest
changes due to changes in choice of mesh; ideally the model should not be highly dependent on
mesh choice
What is an h convergence, why is it called h-convergence - ✔✔mesh refinement to add D.O.F.,
element size h is modified (reduced) globally or locally(mesh controls); named from element
characteristion dimension „h‟ which changes with each iteration
What are criteria of convergence analysis - ✔✔Conditions that must be satisfied for the
convergence process to stop; used for h/p-adaptive solution studies; results: less than 1%
difference
What is the p-convergence, why is it called p-convergence - ✔✔increasing element order with
each iteration until acceptable solution found, mesh element size unaffected; named from p-
order of polynomial function of displacement field
What is calculated in modal analysis - ✔✔-Frequency(natural/resonant) and associated
modes(shapes) of vibration; -can NOT calculate absolute displacement or stresses, only relative
displacementWhat is calculated in linear buckling analysis?
What is calculated in linear buckling analysis? - ✔✔Buckling load factor, buckling mode(shape),
Negative buckling load factor(reverse load and multiply by factor for buckling); -can NOT
calculate displacement
