There are the practical and engineering approaches used to design products. Both have their important place in the world of design. With experience most products usually use the practical approach since they are not subjected to extreme loading conditions and require no computer analysis. Experience is also used in producing new and complex shaped products usually with the required analytical evaluation that involves minor evaluation of stress-strain characteristics of the plastic materials.

When required the engineering approach is used. It involves the use of applicable to stress-strain static and dynamic load equations and formulas such as those in this book and from engineering handbooks. FEA can help a designer to take full advantage of the unique properties of plastics by making products lighter, yet stronger while at the same time also saving money and time to market. The use of FEA has expanded rapidly over the past decades. Unlike metals, plastics are nonlinear [viscoelastic (Chapters 1 and 2)], so they requite different software for analysis, The early software programs were difficult and complex, but gradually the software for plastics has become easier to use. Graphic displays are better organized and are easier to understand.

FEA consumes less time resulting in shortening the lead-time to less than half. Other advantages include increased accuracy, improving reliability, reducing material costs while reducing the expense of building prototypes and remachining tools. By eliminating excess material, it can save weight. It can simulate what will happen, allowing immediate redesign to prevent premature failure. This capability exists because the computer solves simultaneously hundreds of equations that would take literally years to solve without the computer.

With FEA one constructs a model that reduces a product into simple standardized shapes that are called elements. They are located in common coordinate grid system. The coordinate points of the element corners, or nodes, are the locations in the model where output data are provided. In some cases, special elements can also be used that provide additional nodes along their length or sides. The node stiffness properties are identified. They are arranged into matrices and are loaded into a computer. To calculate displacements and strains imposed by the loads on the nodes the computer processes the applied loads. This modeling technique establishes the structural locations where stresses will be evaluated. A cost-effective model concentrates on the smallest elements at areas of highest stress. This configuration provides greater detail in areas of major stress and distortion, and minimizes computer time in analyzing regions of the component where stresses and local distortions are smaller.

Modeling can set up problems because the process of separating a component into elements is not essentially straightforward. Some degree of personal insight, along with an understanding of how materials behave under strain, is required to determine the best way to model a component for FEA. The procedure can be made easier by setdng up a few ground rules before attempting to construct the model. An inadequate model could be quite expensive in terms of computer time. As an example if a component is modeled inadequately for a given problem, the resulting computer analysis could be quite misleading in its prediction of areas of maximum strain and maximum deflection.

For a plane stress analysis, if possible quadrilateral elements should be used. These elements provide better accuracy than the more popular corresponding triangular elements without adding significandy to calculation time. Element size should be in inverse proportion to the anticipated strain gradient with the smallest elements in regions of highest strain. The 2-D and 3-D elements should have corners that are approximately right-angled. They should resemble squares and cubes as much as possible in regions of high strain gradient.

Models used for reinforced plastic (RP) tanks normally range from 1000 to 10,000 elements. Each element is defined by nodes ranging from 3 to 8 per element for a typical shell element. Depending on the type of element, each node will have a given number of degrees of freedom. A 3-D shell element can have 6 degrees of freedom at each node, 3 degrees of translation, and 3 degrees of rotation. Each degree of freedom is described by an equation. Thus, the solution of a finite element evaluation requires the simultaneous solution of a set of equations equal to the number of degrees of freedom.

The RP tank shell element model with 10,000 elements will have more than 50,000 degrees of freedom. Solving such a huge set of equations in a reasonable amount of time, even with the most refined of matrix techniques, requires a great deal of computational power.


Viewing many imaginative variations would blunt the opportunity for creative design by viewing many imaginative variations if each variation introduced a new set of doubts as to its ability to withstand whatever stress might be applied. From this point of view the development of computer graphics has to be accompanied by an analysis technique capable of determining stress levels, regardless of the shape of the part. This need is met by FEA.

Structural Analysis

The FEA computer-based technique determines the stresses and deflections in a structure. Essentially, this method divides a structure into small elements with defined stress and deflection characteristics. The method is based on manipulating arrays of large matrix equations that can be realistically solved only by computer. Most often, FEA is performed with commercial programs. In many cases these programs require that the user know only how to properly prepare the program input.

FEA is applicable in several types of analyses. The most common one is static analysis to solve for deflections, strains, and stresses in a structure that is under a constant set of applied loads. In FEA material is generally assumed to be linear elastic, but nonlinear behavior such as plastic deformation, creep, and large deflections also are capable of being analyzed. The designer must be aware that as the degree of anisotropy increases the number of constants or moduli required describing the material increases.

Uncertainty about a material's properties, along with a questionable applicability of the simple analysis techniques generally used, provides justification for extensive end use testing of plastic products before approving them in a particular application. As the use of more FEA methods becomes common in plastic design, the ability of FEAs will be simplified in understanding the behavior and the nature of plastics.

FEA does not replace prototype testing; rather, the two are complementary in nature. Testing supplies only one basic answer about a design that either passed or failed. It does not quantify results, because it is not possible to know from testing alone how close to the point of passing or failing a design actually exists. FEA does, however, provide information with which to quantify performance.

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