Topology optimization has become an effective tool for least-weight and performance design, especially in aeronautics and aerospace engineering. The purpose of this paper is to survey recent advances of topology optimization techniques applied in aircraft and aerospace structures design. This paper firstly reviews several existing applications: (1) standard material layout design for airframe structures, (2) layout design of stiffener ribs for aircraft panels, (3) multi-component layout design for aerospace structural systems, (4) multi-fasteners design for assembled aircraft structures. Secondly, potential applications of topology optimization in dynamic responses design, shape preserving design, smart structures design, structural features design and additive manufacturing are introduced to provide a forward-looking perspective.

Topology Optimization in Aircraft and Aerospace Structures Design

Review of Degradation Models for Progressive Failure Analysis of Fiber Reinforced Polymer Composites

The postbuckling behaviour of a panel with blade-stiffeners incorporating tapered flanges was experimentally investigated. A new failure mechanism was identified for this particular type of stiffener. Failure was initiated by mid-plane delamination at the free edge of the postbuckled stiffener web at a node-line. This was consistent with an interlaminar shear stress failure and was calculated from strain gauge measurements using an approximate analysis based on lamination theory and incorporating edge effects. The critical shear stress was found to agree well with the shear strength obtained from a three-point bending test of the web laminate.

Postbuckling behaviour of a blade-stiffened composite panel loaded in uniaxial compression

A finite element procedure is presented for the analysis of the buckling and postbuckling behavior of cracks in plates loaded in tension. The procedure proposed is applied to the problem of the centrally cracked plate in tension where the loading direction is perpendicular to the crack faces. The results of the analysis show that the buckling deformations can cause a considerable amplification of the stress intensity around the crack tip. This effect, which is due to a redistribution of the stress field in the plate, increases with the length of the crack.

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The buckling behavior of a central crack in a plate under tension

This paper presents an extension of the dual boundary element method to analysis of crack growth in plates loaded in combine bending and tension. Five stress intensity factors, two for membrane behaviour and three for shear deformable plate bending are computed using the J-Integral technique. Crack growth processes are simulated with an incremental crack extension analysis based on the maximum principal stress criterion. The method is considered effective since no remeshing is required and the crack extension is modelled by adding new boundary elements to the previous crack boundaries. Several incremental crack growth analysis for different configurations and loadings are presented.

Crack Growth analysis of plates Loaded by bending and tension using dual boundary element method

The crack tip stress fields for plate bending and membrane loading problems are reviewed and the four stress intensity factors that determine these fields are defined. These four stress intensity factors arise from use of Kirchhoff plate theory to account for the bending loads and two dimensional plane stress elasticity to account for the membrane loads. The energy release rate is related to the stress intensity factors and to the stress resultants of plate theory. Virtual crack extension, nodal release and modified crack closure integral methods are discussed for computing components of the energy release rate from finite element analyses of cracked plates. Sample computations of stress intensity factors for single and mixed mode cases are presented for a crack in an infinite plate. Sample computations of stress intensity factors for a double edge notched tension-torsion test specimen are given as well.

Computation of membrane and bending stress intensity factors for thin, cracked plates

Non-linear analyses are difficult simulations to perform and place increased demands not only on the computational systems but also on the analyst. The number of possible problems and/or difficulties increases significantly compared to those for linear elastic analyses. Combined material and geometric non-linearities challenge the analyst and the solution algorithms. Progressive failure and damage propagation for composite structures result in even more complexities due to the discrete, abrupt changes in local material stiffness. Analysts need to interrogate the computed solutions carefully based on their understanding of structural mechanics, material behavior, computational procedures and non-linear phenomena to distill correct physics from such simulations. This paper describes the computational strategy incorporated into the STAGS non-linear finite element analysis code with special emphasis on progressive failure analysis of laminated composite structures. Results for selected laminated composite structures are used to demonstrate the PFA capability.

STAGS computational procedure for progressive failure analysis of laminated composite structures

PANDA2 is a computer program for the minimum weight design of stiffened composite, flat or cylindrical, perfect or imperfect panels and shells subject to multiple sets of combined in-plane loads, normal pressure, edge moments and temperature. STAGS is a general nonlinear finite element code that is specifically designed to analyze especially difficult stability problems in shell structures. Weight optimization of stiffened panels can be particularly troublesome when local buckling is allowed to occur in the pre-collapse state. For these systems, designs may be affected by interaction between local modes, a mechanism that manifests itself as mode jumping and is difficult to characterize. In this paper we describe how in PANDA2 mode jumping is detected and suppressed in optimized panels. Two axially compressed blade stiffened panels optimized by PANDA2 for service in the far postbuckling regime were numerically tested by STAGS. Mode jumping was permitted to occur below the design load in the first panel and suppressed in the second. Results obtained by STAGS are in reasonably good agreement with predictions by PANDA2. The first panel exhibits mode jumping well below the design load. Application of STAGS to this panel reveals that even though the mode jump involves little change in potential energy it generates large amplitude oscillating stresses with significant stress reversal that might well cause fatigue and delamination. The oscillating stresses are caused by postbuckling lobes moving to and fro

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Optimization of Stiffened Panels in which Mode Jumping is Accounted for

The capability of the computer program PANDA2 to generate minimum-weight designs of stiffened panels and cylindrical shells is enhanced to permit the adding of substiffeners with rectangular cross sections between adjacent major stringers and rings. As a result many new buckling margins exist that govern buckling over various domains and subdomains of the doubly stiffened panel or shell. These generally influence the evolution of the design during optimization cycles. The substiffeners may be stringers and/or rings or may form an isogrid pattern. The effects of local, inter-ring, and general buckling modal imperfections can be accounted for during optimization. Perfect and imperfect cylindrical shells with external T-shaped stringers and T-shaped rings and with and without substringers and subrings and under combined axial compression, external pressure, and in-plane shear are optimized by multiple executions of a "global" optimizer called SUPEROPT. It is found that from the point of view of minimum weight there is little advantage of adding substiffeners. However, with substiffeners present the major stringers and rings are spaced farther apart at the optimum design than is so when there are no substiffeners. The weight of a cylindrical shell with substiffeners is much less sensitive to the spacing of the major T-shaped stringers than is the case for a cylindrical shell without substiffeners. The optimum designs obtained by PANDA2 are evaluated by comparisons with buckling loads obtained from a general-purpose finite element program called STAGS. Predictions from STAGS agree well with those from PANDA2.

Charles Rankin

Papers

Computation of membrane and bending stress intensity factors for thin, cracked plates

STAGS computational procedure for progressive failure analysis of laminated composite structures

Optimization of Stiffened Panels in which Mode Jumping is Accounted for

Optimum Design of Stiffened Panels With Substiffeners

Nonlinear response of damaged stiffened shells subjected to combined internal pressure and mechanical loads