Analyzing structural durability in the frequency domain

• US 9,020,786 B2
• Filed: 11/30/2007
• Issued: 04/28/2015
• Est. Priority Date: 03/14/2006
• Status: Active Grant

• Current Assignee: The Boeing Co.
• Original Assignee: The Boeing Co.
• Inventors: Rassaian, Mostafa, Gosse, Jonathan H., Christensen, Stephen
• Primary Examiner(s): Fernandez Rivas, Omar
• Assistant Examiner(s): CALLE, ANGEL J.
• Application Number:
  US11/948,880
• Publication Number:
  US 20090144038A1
• Time in Patent Office: 2,706 Days
• Field of Search: 703/6, 703/7, 702/34, 702/50, 702/182
• US Class Current: 703/6
• CPC Class Codes: B29C 66/721 Fibre-reinforced materials B29C66/729 takes precedence
• CPC Class Codes: B29C 66/7212 characterised by the composition of the fibres
• CPC Class Codes: B64C 2001/0072 from composite materials
• CPC Class Codes: G01N 2291/02827 Elastic parameters, strength or force
• CPC Class Codes: G01N 29/045 by imparting shocks to the workpiece and detecting the vibrations or the acoustic waves caused by the shocks measuring resonant frequency G01H13/00; measuring strength properties by application of mechanical stress G01N3/00
• CPC Class Codes: G01N 29/12 by measuring frequency or resonance of acoustic waves measuring frequency or resonant frequency of mechanical vibrations or acoustic waves in general G01H1/06, G01H3/04, G01H13/00; acoustic resonators G10K11/04; vibration or shock testing of structures G01M7/00
• CPC Class Codes: G01N 3/32 by applying repeated or pulsating forces
• CPC Class Codes: G06F 2113/26 Composites
• CPC Class Codes: G06F 30/15 Vehicle, aircraft or watercraft design
• CPC Class Codes: G06F 30/17 Mechanical parametric or variational design
• CPC Class Codes: G06F 30/20 Design optimisation, verification or simulation optimisation, verification or simulation of circuit designs G06F30/30
• CPC Class Codes: G06F 30/23 using finite element methods [FEM] or finite difference methods [FDM]
• CPC Class Codes: Y02T 50/40 Weight reduction

Abstract

A method of analyzing the durability of a structure. Load-controlled testing is performed on samples of a composite material of the structure to relate critical strain invariants of the material to cyclic rates of strain invariant accumulation and frequencies associated with the cyclic rates. The material is characterized based on effective properties of the material, including the cyclic rates of strain invariant accumulation. Laminate properties and a geometrical definition of the structure are used to obtain a parametric model. Material characterizations are used to determine model element frequency responses to applied load conditions. Each element'"'"'s frequency responses and critical strain invariants are used to determine whether damage is indicated at the element. Progression of damage is tracked and accounted for in the model.

Claims

1. A method of analyzing a durability of a structure through a plurality of operations comprising:

for each one of a plurality of materials of the structure, performing load-controlled testing on one or more samples of each one of the plurality of materials to relate each of a plurality of critical strain invariants of each one of the plurality of materials to cyclic rates of strain invariant accumulation and frequencies associated with the cyclic rates;

characterizing each of the plurality of materials based on effective properties of each of the plurality of materials to obtain material characterizations, the effective properties including the cyclic rates of strain invariant accumulation of each one of the plurality of materials;

using the effective properties of each of the plurality of materials and a geometrical definition of the structure to obtain a parametric model including a plurality of elements;

applying load conditions to the parametric model;

using the material characterizations to determine frequency responses of the plurality of elements to the load conditions; and

for each one of the plurality of elements, using the determined frequency responses and the plurality of critical strain invariants to determine whether damage is indicated at each one of the plurality of elements.

2. The method of claim 1, further comprising:

using strain tensors of the each one of the plurality of elements to analyze progression of indicated damage relative to the each one of the plurality of elements; and

accounting for the progression in the parametric model.

3. The method of claim 1, wherein the performing load-controlled testing comprises applying quasi-static and/or cyclic loading to one or more of the samples until a point of failure is reached to determine one of the plurality of critical strain invariants.

4. The method of claim 1, wherein the applying load conditions to the parametric model comprises applying at least one of the following:

a base excitation, a shock, an acoustic load and a preload.

5. The method of claim 1, wherein at least one of the plurality of materials comprises a composite material.

6. The method of claim 1, wherein the applying load conditions to the parametric model comprises representing sound pressure level (SPL) as power spectrum density relative to frequency.

7. The method of claim 1, wherein the using the determined frequency responses and the plurality of critical strain invariants to determine whether damage is indicated at each one of the plurality of elements comprises using a strain invariant failure theory of analysis to analyze progression of strain to a point of damage onset.

8. A system for analyzing a durability of a structure, the system comprising at least one processor and memory configured to:

characterize each of a plurality of materials of the structure based on effective properties of the plurality of materials to obtain material characterizations, the effective properties including, for each of a plurality of critical strain invariants of the plurality of materials, a plurality of cyclic rates of strain invariant accumulation and frequencies associated with the plurality of cyclic rates of strain invariant accumulation of each one of the plurality of materials;

use the effective properties of the plurality of materials and a geometrical definition of the structure to obtain a parametric model including a plurality of elements;

apply load conditions to the parametric model;

use the material characterizations to determine frequency responses of the plurality of elements to the load conditions, and

for each one of the plurality of elements, use the determined frequency responses and the plurality of critical strain invariants to determine whether damage is indicated at each one of the plurality of elements.

9. The system of claim 8, wherein the characterizing of each of the plurality of materials comprises using results of load-controlled testing on one or more samples of each of the plurality of materials to determine at least some of the effective properties.

10. The system of claim 9, wherein the load-controlled testing comprises applying quasi-static and/or cyclic loading to the one or more samples until a point of failure is reached to determine one of the plurality of critical strain invariants.

11. The system of claim 8, wherein the at least one processor and memory further configured to:

use strain tensors of the plurality of elements to analyze progression of indicated damage relative to each one of the plurality of elements; and

account for the progression in the parametric model.

12. The system of claim 8, wherein the load conditions to the parametric model comprise at least one of the following:

a base excitation, a shock, an acoustic load and a preload.

13. The system of claim 8, wherein at least one of the plurality of materials comprises a composite material.

14. The system of claim 8, wherein the at least one processor and the memory further configured to represent sound pressure level (SPL) as power spectrum density relative to frequency.

15. The system of claim 8, wherein the at least one processor and the memory further configured to use a strain invariant failure theory of analysis to analyze progression of loading effects in the plurality of materials to and beyond a point of damage onset.

16. A non-transitory, machine-readable medium stored on a memory, for use in analyzing a durability of a structure, the machine-readable medium configured for:

characterizing each of one of a plurality of materials of the structure based on effective properties of each one of the plurality of materials to obtain material characterizations, the effective properties including, for each of a plurality of critical strain invariants of each one of the plurality of materials, a plurality of cyclic rates of strain invariant accumulation and frequencies associated with the plurality of cyclic rates of strain invariant accumulation of each one of the plurality of materials;

using the effective properties of the plurality of materials and a geometrical definition of the structure to obtain a parametric model including a plurality of elements;

applying load conditions to the parametric model;

using the material characterizations to determine frequency responses of the plurality of elements to the load conditions;

for each one of the plurality of elements, using the determined frequency responses and the plurality of critical strain invariants to determine whether damage is indicated at each one of the plurality of elements;

using strain tensors of the plurality of elements to analyze progression of indicated damage relative to the plurality of elements; and

accounting for the progression in the parametric model.

17. The machine-readable medium of claim 16, further comprising computer-executable instructions for using a strain invariant failure theory of analysis to analyze progression of loading effects in the plurality of materials to and beyond a point of damage onset.

18. The machine-readable medium of claim 16, further comprising computer-executable instructions for applying at least one of the following:

a base excitation, a shock, a preload, and an acoustic load.

19. The machine-readable medium of claim 16, further comprising computer-executable instructions for analyzing progression of indicated damage relative to the plurality of elements, wherein the analyzing progression of the indicated damage performed with reference to a frequency domain.

20. The machine-readable medium of claim 16, further comprising computer-executable instructions for performing mode superposition and/or mode acceleration analysis to analyze effects of the load conditions.