Basic Concepts of Analysis

The software uses the Finite Element Method (FEM). FEM is a numerical technique for analyzing engineering designs. FEM is accepted as the standard analysis method due to its generality and suitability for computer implementation. FEM divides the model into many small pieces of simple shapes called elements effectively replacing a complex problem by many simple problems that need to be solved simultaneously.

 CAD model of a part Model subdivided into small pieces (elements)

Elements share common points called nodes. The process of dividing the model into small pieces is called meshing.

The behavior of each element is well-known under all possible support and load scenarios. The finite element method uses elements with different shapes.

The response at any point in an element is interpolated from the response at the element nodes. Each node is fully described by a number of parameters depending on the analysis type and the element used. For example, the temperature of a node fully describes its response in thermal analysis. For structural analyses, the response of a node is described, in general, by three translations and three rotations. These are called degrees of freedom (DOFs). Analysis using FEM is called Finite Element Analysis (FEA).

 A tetrahedral element. Red dots represent nodes. Edges of an element can be curved or straight

The software formulates the equations governing the behavior of each element taking into consideration its connectivity to other elements. These equations relate the response to known material properties, restraints, and loads.

Next, the program organizes the equations into a large set of simultaneous algebraic equations and solves for the unknowns.

In stress analysis, for example, the solver finds the displacements at each node and then the program calculates strains and finally stresses.

The software offers the following types of studies:

• Static (or Stress) Studies. Static studies calculate displacements, reaction forces, strains, stresses, and factor of safety distribution. Material fails at locations where stresses exceed a certain level. Factor of safety calculations are based on one of four failure criterion.

Static studies can help you avoid failure due to high stresses. A factor of safety less than unity indicates material failure. Large factors of safety in a contiguous region indicate low stresses and that you can probably remove some material from this region.

• Frequency Studies. A body disturbed from its rest position tends to vibrate at certain frequencies called natural, or resonant frequencies. The lowest natural frequency is called the fundamental frequency. For each natural frequency, the body takes a certain shape called mode shape. Frequency analysis calculates the natural frequencies and the associated mode shapes.

In theory, a body has an infinite number of modes. In FEA, there are theoretically as many modes as degrees of freedom (DOFs). In most cases, only a few modes are considered.

Excessive response occurs if a body is subjected to a dynamic load vibrating at one of its natural frequencies. This phenomenon is called resonance. For example, a car with an out-of-balance tire shakes violently at a certain speed due to resonance. The shaking decreases or disappears at other speeds. Another example is that a strong sound, like the voice of an opera singer, can cause a glass to break.

Frequency analysis can help you avoid failure due to excessive stresses caused by resonance. It also provides information to solve dynamic response problems.

• Dynamic Studies. Dynamic studies calculate the response of a model due to loads that are applied suddenly or change with time or frequency.

Linear dynamic studies are based on frequency studies. The software calculates the response of the model by accumulating the contribution of each mode to the loading environment. In most cases, only the lower modes contribute significantly to the response. The contribution of a mode depends on the load’s frequency content, magnitude, direction, duration, and location.

The objectives of a dynamic analysis include: (a) the design of structural and mechanical systems to perform without failure in dynamic environments, and (b) the reduction of vibration effects.

• Buckling Studies. Buckling refers to sudden large displacements due to axial loads. Slender structures subject to axial loads can fail due to buckling at load levels lower than those required to cause material failure. Buckling can occur in different modes under the effect of different load levels. In many cases, only the lowest buckling load is of interest.

• Thermal Studies. Thermal studies calculate temperatures, temperature gradients, and heat flow based on heat generation, conduction, convection, and radiation conditions. Thermal studies can help you avoid undesirable thermal conditions like overheating and melting.

• Design Studies. Optimization design studies automate the search for the optimum design based on a geometric design. The software is equipped with a technology to quickly detect trends and identify the optimum solution using the least number of runs. Optimization design studies require the definition of the following:

• Goals or Objectives. State the objective of the study. For example, minimum material to be used.

• Design Variables. Select the dimensions that can change and set their ranges. For example, the diameter of a hole can vary from 0.5” to 1.0” while the extrusion of a sketch can vary from 2.0” to 3.0”.

• Constraints. Set the conditions that the optimum design must satisfy. For example, you can require that a stress component does not exceed a certain value and the natural frequency to be within a specified range.

NOTE: For the non-optimization design study, do not define any goals.

• Nonlinear Studies. When the assumptions of linear static analysis do not apply, you can use nonlinear studies to solve the problem. The main sources of nonlinearity are: large displacements, nonlinear material properties, and contact. Nonlinear studies calculate displacements, reaction forces, strains, and stresses at incrementally varying levels of loads and restraints. When inertia and damping forces can not be ignored, you can use nonlinear dynamic analysis.

Nonlinear studies refer to nonlinear structural studies. For thermal studies, the software automatically solves a linear or nonlinear problem based on material properties and thermal restraints and loads.

Solving a nonlinear problem requires much more time and resources than solving a similar linear static study.

The principle of superposition does not apply for nonlinear studies. For example, If applying force F1 causes stress S1 and applying force F2 causes stress S2 at a point, then applying the forces together does NOT necessarily cause a stress (S1+S2) at the point as is the case for linear studies.

Nonlinear studies can help you assess the behavior of the design beyond the limitations of static and buckling studies.

Static studies offer a nonlinear solution for contact problems when you activate the large displacement option.

• Drop Test Studies. Drop test studies evaluate the effect of dropping the design on a rigid floor. You can specify the dropping distance or the velocity at the time of impact in addition to gravity. The program solves a dynamic problem as a function of time using explicit integration methods. Explicit methods are fast but require the use of small time increments. Due to the large amount of information the analysis can generate, the program saves results at certain instants and locations as instructed before running the analysis.

After the analysis is completed, you can plot and graph displacements, velocities, accelerations, strains, and stresses.

• Fatigue Studies. Repeated loading weakens objects over time even when the induced stresses are considerably less than allowable stress limits. The number of cycles required for fatigue failure to occur at a location depends on the material and the stress fluctuations. This information, for a certain material, is provided by a curve called the S-N curve. The curve depicts the number of cycles that cause failure for different stress levels. Fatigue studies evaluate the consumed life of an object based on fatigue events and S-N curves.

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