10.25394/PGS.7789097.v1
Ning Liu
Global and Local Buckling Analysis of Stiffened and Sandwich Panels Using Mechanics of Structure Genome
2019
Purdue University Graduate School
Mechanics of Structure Genome
Bloch wave theory
constitutive modeling
instability
buckling
post buckling
Newton's method
arc length
stiffened panels
sandwich panels
finite element analysis
representative volume elements
2019-06-10 16:59:49
article
https://hammer.figshare.com/articles/Global_and_Local_Buckling_Analysis_of_Stiffened_and_Sandwich_Panels_Using_Mechanics_of_Structure_Genome/7789097
Mechanics of structure genome (MSG) is a unified homogenization theory that
provides constitutive modeling of three-dimensional (3D) continua, beams and plates.
In present work, the author extends the MSG to study the buckling of structures such
as stiffened and sandwich panels. Such structures are usually slender or flat and easily
buckle under compressive loads or bending moments which may result in catastrophic
failure.<div><br><div>Buckling studies of stiffened and sandwich panels are found to be scattered. Most
of the existed theories employ unnecessary assumptions or only apply to certain types
of structures. There are few unified approaches that are capable of studying the
buckling of different kinds of structures altogether. The main improvements of current
approach compared with other methods in the literature are avoiding unnecessary
assumptions, the capability of predicting all possible buckling modes including the
global and local buckling modes, and the potential in studying the buckling of various
types of structures.<br></div><div><br></div><div>For global buckling that features small local rotations, MSG mathematically decouples
the 3D geometrical nonlinear problem into a linear constitutive modeling using
structure genome (SG) and a geometrical nonlinear problem defined in a macroscopic
structure. As a result, the original structures are simplified as macroscopic structures
such as beams, plates or continua with effective properties, and the global buckling
modes are predicted on macroscopic structures. For local buckling that features
finite local rotations, Green strain is introduced into the MSG theory to achieve geometrically nonlinear constitutive modeling. Newtonâ€™s method is used to solve
the nonlinear equilibrium equations for fluctuating functions. To find the bifurcated
fluctuating functions, the fluctuating functions are then perturbed under the Bloch-periodic
boundary conditions. The bifurcation is found when the tangent stiffness
associated with the perturbed fluctuating functions becomes singular. Moreover, the
arc-length method is introduced to solve the nonlinear equilibrium equations for post-local-buckling
predictions because of its robustness. The imperfection is included in
the form of geometrical imperfection by superimposing the scaled buckling modes in
linear perturbation analysis on mesh.<br></div><div><br></div><div>Extensive validation case studies are carried out to assess the accuracy of the
MSG theory in global buckling analysis and post-global-buckling analysis, and assess
the accuracy of the extended MSG theory in local buckling and post-local-buckling
analysis. Results using MSG theory and extended MSG theory in buckling analysis
are compared with direct numerical solutions such as 3D FEA results and results in
literature. Parametric studies are performed to reveal the relative influence of selective
geometric parameters on buckling behaviors. The extended MSG theory is also
compared with representative volume element (RVE) analysis with Bloch-periodic
boundary conditions using commercial finite element packages such as Abaqus to
assess the efficiency and accuracy of the present approach.<br></div></div>