Structural and Multidisciplinary Optimization

, Volume 56, Issue 3, pp 697–712 | Cite as

Global sensitivity analysis for fiber reinforced composite fiber path based on D-MORPH-HDMR algorithm

INDUSTRIAL APPLICATION
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Abstract

This study presents a quantitative sensitivity analysis for the assessment of fiber reinforced composites (FRCs). Global sensitivity analysis (GSA) approach is based on the variance based method incorporating Random Sampling-High Dimensional Model Representation (RS-HDMR) expansion in which component functions are determined by diffeomorphic modulation under observable response preserving homotopy (D-MORPH) regression. The advantage of the D-MORPH regression lies in its capability to solve linear algebraic equations with a limited number of sample points. The main purpose is to investigate the influence of fiber path, regarded as the design variable, on the formability and structural performance of FRCs. Wherein, spring-back and load-carrying capacity are two meaningful problems to be addressed. Two typical FRCs are included that an L-shaped part with straight fiber path using autoclave manufacturing process and a variable stiffness composite cylindrical shell under pure bending. The work not only focuses on the ranking of design variables but also hopes to find out their interactions represented by the second order global sensitivity indexes. After being tested by three typical numerical functions, the GSA algorithm highlights that spring-back of FRC using autoclave manufacturing process is most sensitive to fiber orientation angles on plies close to the tool. And buckling performance of the VS cylinder is dominated by fiber orientation angles at compression/tension regions.

Keywords

Composite Spring-back Variable stiffness Global sensitivity analysis RS-HDMR D-MORPH 

Nomenclature

GSA

Global sensitivity analysis

GSI

Global sensitivity index

D-MORPH

Diffeomorphic Modulation Under Observable Response Preserving Homotopy

RS-HDMR

Random Sampling High Dimensional Model Representation

χi

ith input variable

χ

Input variable vector,χ = (χ 1, χ 2,  ⋯ , χ d )

ρ(χ)

Output response

Kd

K d  = {(χ 1, χ 2,  ⋯ , χ d )|0 ≤ χ i  ≤ 1, i = 1, 2,  ⋯ , d}

k , l , m , t

Integers

N

Total number of sample points

\( {S}_i/{S}_{i j},{S}_i^T \)

First/second order GSI and total effect index

φ(χ)

Orthonormal polynomial basis

α , β

Undetermined coefficients in HDMR expansion’s component function

Q

Cost function

c

Vector containing all undetermined coefficients

B

Weight matrix of the cost function

γ

Fiber orientation angle for VS composite cylinder

κ

Angle

T

Design variable of fiber orientation angle

ρspring − back

Spring-back for the L-shaped composite part

ρcr

Critical buckling load for the VS composite cylinder

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Notes

Acknowledgements

This work has been supported by Project of the Key Program of National Natural Science Foundation of China under the Grant Numbers 11572120, 11302266.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.State Key Laboratory of Advanced Design and Manufacturing for Vehicle BodyHunan UniversityHunanChina
  2. 2.Joint Center for Intelligent New Energy VehicleShanghaiChina

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