Civil Engineering Reference
In-Depth Information
Chapter 5
Stochastic Finite Element and Satellite
Structure Design
Abstract Throughout design development of satellite structure, stress engineer is
usually challenged with randomness in applied loads and material properties. To
overcome such problem, a risk-based design is applied which estimates satellite
structure probability of failure under static and thermal loads. Determining prob-
ability of failure can help to update initially applied factors of safety that were used
during structure preliminary design phase. These factors of safety are related to the
satellite mission objective. Sensitivity-based analysis is to be implemented in the
context of finite element analysis (probabilistic finite element method or stochastic
finite element method (SFEM)) to determine the probability of failure for satellite
structure or one of its components.
5.1 Introduction to Stochastic Finite Element
Theory
The concept of risk-based design was introduced by Freudenthal [
1
] and was
summarized by Freudenthal et al. [
2
]. Considering the load on structure, S, and the
resistance of the structure, R are random in nature. Their randomness can be
defined by their means and standard deviations and corresponding probability
density functions, f
S
(s), f
R
(r). The objective of safe design in deterministic design
procedures can also be achieved by selecting the design variables so that the area
of overlap between the two probability density functions is as small as possible.
The area of overlap depends on the relative positions of the two curves (mean
value of the two variables), the dispersion of the two variables (standard devia-
tion), and the shape of the curves (normal, lognormal, or beta distribution).
Deterministic design approaches achieve this objective by shifting the positions of
the curves through the use of safety factors. A more rational approach would be to
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