A.2.5 有限元素分析

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A.2.5 Finite Element Analysis
A.2.5.1 Desription and Purpose
Finite element analysis is a computer-based numerical method for analysing the effects of applied loads to physical items.  Load can be mechanical, thermal, electromagnetic, fluid, or combination of these.  Usually the problem addressed is too complex for classical methods.

This technique differs fundamentally from classical methods in terms of its treatment of an item.  The infinitesimal differential elements used in calculus, differential and partial differential equations consider the item as a continuum.  For finite element analysis, the item is divided into simple interrelated building blocks called elements.  Elements are characterized by shape functions.  Collectively, they form a geometric model of the item.  Elements are interconnected at nodes.  Information in passed from element to element only at the level of common nodes.  Interpolation is used to assume continuity within elements and across element boundaries. Thus, effects at any point within the item can be expressed in terms of nodal displacements.  

A.2.5.2 Application
Finite element analysis is an effective method for predicting behaviour and failure moded in complex structures.  It can be used for analysing many dffierent types of problemds, including mechnical stress analysis, vibration, fluid flow, heat transfer, electromagnetic filelds and others.  

A.2.5.3 Key Element (Steps)
- Select the most appropriate type of finite elements for modelling the item.  
- Divide the item into elements and define element properties.
- Assemble a matrix representation of the interaction among the degrees of freedom of the nodes.
- Define boundary conditions and apply loads.  
- Solve the set of algebraic equations for the matrix to calculate nodal displacements.  
- Calulate physical parameters of interest, e.g., stress, vibrational modes.  

A.2.5.4 Benefits
- Can be used for analysing both elasticand inelastic effects.  
- Can be used for performing both static and dynamic analyses.  
- Can be used to analyze items with irregular shapes, multiple boundary conditions and loads as well as various materials.  
- Can be used to optimize designs.  
- Can be used to assess and validate reliability.  

A.2.5.5 Limitations
- Requires a high level of specialized technical expertise.  
- Easy to misinterpret or misapply results.  

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Finite Element Analysis (FEA)

RBPR-3: Design for Reliability:  
Purpose: Simulation approaches are effective checks of the mechanical and thermal robustness of designs prior to hardware availability.  They enable effective trade-offs of design alternatives in a rapid manner.  

Application Guidance:
Items to be analyzed should be carefully selected due to the cost of the task.  Selection criteria may include items with little or no prior experience base, state-of-the-art design or packaging concepts, extreme environmental exposure, or critical  thermal/mechanical performance or behaviour constraints.  



BPR-3: Design for Reliability: Finite Element Analysis
Description:
Determining the mechanical stresses present in products through simulation by decomposing the product into simple elements.  

Advantage:
Stress response for new or unique components.

Disadvantage:
Very high cost to perform for many items.


3.3.17 Finite Element Analysis
3.3.17.1 Purpose.  
Simulation techniques provide very effective assessments of mechanical and thermal robustness of product design prior to production.  Finite Element Analysis (FEA) is a simulation technique, usually computer implemented, that estimates material response to loads or environmental exposure.  The analysis can be used as a design tool to asses the potential for thermal or mechanical failure in reaction to the expected loads before manufacturing or testing of the product take place.  

3.3.17.2 Benefits
The benefits of a Finite Element Analysis are the early discovery of life limiting material deficiencies or the uncovering of excess loading conditions.  With the identification of the deficiency, either more robust components or isolation techniques can be introduced to reduce the load's impact on the product design reliability before production decisions are finalized.  This design analysis can be proformed before product manufacturing to uncover problems and to analyze solutions without requiring the testing of materials.  

3.17.3 Timing
The most effect FEA occurs when the product or item is developed to the point where the material and design properties can be clearly defined.  This suggests a time frame after preliminary design Concept/Planning and before completion of the product Design/Development phase.  Since Finite Element Analysis are time consuming and costly, the items to be analyzed should be selected very carefully.  Performed during the design phase, this analysis can identify problems which could cause catastrophic failure events.  

3.3.17.4 Application Guidelines
A Finite Element Anlaysis is the breakdown of a product into one or more elements that can be presented by mathematical models of an idealized structure.  Each structure is represented b a grid of node points with interconnections.  Without the use of computers to solve these models, the technique is restricted to the most simple or ideal problems.  With the use of high speed digital computers, the scope of this analysis has been expanded to analyze complex items such as very high speed integrated circuits (VHSIC) for mechanical displacement resulting from a mismatch of thermal coefficients of expansion relative to the circuit board.  With the use of a computer, a solution can be obtained by combining individual elements into an idealized structure for which conditions of equilibrium and compatibility are satistied.  
The most difficult and time consuming part of any Finite Element Analysis is establishing the detailed mathematical models and conditions.  Therefore, selection of items to be analyzed should be performed very carefully.  Selection criteria should include:  
- New materials or techniques.
- Severe environmental load conditions.
- Critical thermal or mechanical constraints.  
The general steps to be followed in performing the FEA are:
1. Idealize the product into an analyzable form
2. Reduce the coarse mesh to a small area (or single device) to determine more accurate stress information
3. Use deterministic life analysis using stress and cycles to failure
4. Determine a probability of success based on the statistical distribution of failure resulting from the stress and cycles

RBPR-4: Assessing Reliability Progress:
Finite Element Anlaysis
Description:
Determine the mechanical stresses present in products through simulation by decomposing the product into simple elements.  

Purpose:
Assesses the ability of the design to withstand thermal and mechanical stresses using simulation techniques.  

Application Guidance:
Use for designs that are unproven with little prior experience/test data, that use advanced/unique packaging/design concepts, or will encounter servere environmental loads.  



4.3.11 Finite Element Analysis
4.3.11.1 Purpose
Simulation techniques are very effective checks of mechanical and thermal robustness of product designs prior to production.  Finite Element Analysis (FEA) is a simulation technique, usually computer implemented, the estimates material response to loads or environmental disturbances.  The analysis can be used to assess the potential for thermal or mechanical failure in reaction to the expected loads, or assessment of failures resulting from testing.  

4.3.11.2 Benefits
The benefits of a FEA are the early discovery of life limiting material deficiencies and the uncovering of excessive environmental load conditions.  With the identification of the deficiency, either more robust components or better environmental isolation techniques can be introduced to reduce the load's impact on the product design.  This analysis can be performed before product manufacturing to uncover problems, after design changes to detect weaknesses, or after problem areas have been determined through testing.  

4.3.11.3 Timing
The most effective FEA occurs when the product or item is developed to the point where the material and design properties can be clearly defined.  Since EFAs are time consuming and costly, the items to be analyzed should be selected very carefully.  When used as an assessment tool, failure trends or problem areas would be potential candidates for the analysis.  

4.3.11.4 Application Guidelines
A FEA is the breakdown of a product into one or more elements that can be represented by mathematical models of an idealized structure.  Each structure is represented by a grid of node points with interconnections.  Without the use of computers to solve these models, the tehcnique is restricted to the most simple or ideal problems.  With the use of high speed digital computers, the scope of this analysis has been expanded to anaylze complex items such as a liquid cooled high powered traveling wave tube (TWT) for thermal displacement of internal components relative to the tube envelope.  With the use of a computer, a solution can be obtained by combining individual elements into an idealized structure for which conditions of equilibrium and compatibility are satisfied.  
Application of a FEA is especially appropriate for products that use advanced or unique packaging or design concepts.  The types of problems that can be analyzed include mechnical stress analysis, heat transfer, fluid flow, vibration and elasticity.  
The most difficutl and time consuming part of a FEA is establishing the detailed mathematical models and boundary conditions.  Therefore, selection of items to be analyzed should be performed very carefully.  Selection criteria should include:
- New materials or techniques
- Severe environmental load conditions
- Critical thermal or mechanical constraint
- Failure trends
The general steps to be followed in performing FEA are:
1. Idealize the product into an analyzable form
2. Reduce the coarse mesh to a small area (or single device) to determine more accurate stress information
3. Use deterministic life anallysis using stress and cycles to failure
4. Determine a probabilty of success based on the statistical distribution of failure of failure resulting from the stress and cycles