337 research outputs found
Isogeometric analysis for functionally graded microplates based on modified couple stress theory
Analysis of static bending, free vibration and buckling behaviours of
functionally graded microplates is investigated in this study. The main idea is
to use the isogeometric analysis in associated with novel four-variable refined
plate theory and quasi-3D theory. More importantly, the modified couple stress
theory with only one material length scale parameter is employed to effectively
capture the size-dependent effects within the microplates. Meanwhile, the
quasi-3D theory which is constructed from a novel seventh-order shear
deformation refined plate theory with four unknowns is able to consider both
shear deformations and thickness stretching effect without requiring shear
correction factors. The NURBS-based isogeometric analysis is integrated to
exactly describe the geometry and approximately calculate the unknown fields
with higher-order derivative and continuity requirements. The convergence and
verification show the validity and efficiency of this proposed computational
approach in comparison with those existing in the literature. It is further
applied to study the static bending, free vibration and buckling responses of
rectangular and circular functionally graded microplates with various types of
boundary conditions. A number of investigations are also conducted to
illustrate the effects of the material length scale, material index, and
length-to-thickness ratios on the responses of the microplates.Comment: 57 pages, 14 figures, 18 table
Geometrically nonlinear isogeometric analysis of laminated composite plates based on higher-order shear deformation theory
In this paper, we present an effectively numerical approach based on
isogeometric analysis (IGA) and higher-order shear deformation theory (HSDT)
for geometrically nonlinear analysis of laminated composite plates. The HSDT
allows us to approximate displacement field that ensures by itself the
realistic shear strain energy part without shear correction factors. IGA
utilizing basis functions namely B-splines or non-uniform rational B-splines
(NURBS) enables to satisfy easily the stringent continuity requirement of the
HSDT model without any additional variables. The nonlinearity of the plates is
formed in the total Lagrange approach based on the von-Karman strain
assumptions. Numerous numerical validations for the isotropic, orthotropic,
cross-ply and angle-ply laminated plates are provided to demonstrate the
effectiveness of the proposed method
Nonlinear static and transient isogeometric analysis of functionally graded microplates based on the modified strain gradient theory
The objective of this study is to develop an effective numerical model within the framework of an isogeometric analysis (IGA) to investigate the geometrically nonlinear responses of functionally graded (FG) microplates subjected to static and dynamic loadings. The size effect is captured based on the modified strain gradient theory with three length scale parameters. The third-order shear deformation plate theory is adopted to represent the kinematics of plates, while the geometric nonlinearity is accounted based on the von Kármán assumption. Moreover, the variations of material phrases through the plate thickness follow the rule of mixture. By using Hamilton’s principle, the governing equation of motion is derived and then discretized based on the IGA technique, which tailors the non-uniform rational B-splines (NURBS) basis functions as interpolation functions to fulfil the C2-continuity requirement. The nonlinear equations are solved by the Newmark’s time integration scheme with Newton-Raphson iterative procedure. Various examples are also presented to study the influences of size effect, material variations, boundary conditions and shear deformation on the nonlinear behaviour of FG microplates
Modelling of FG-TPMS plates
Functionally graded porous plates have been validated as remarkable
lightweight structures with excellent mechanical characteristics and numerous
applications. With inspiration from the high strength-to-volume ratio of triply
periodic minimal surface (TPMS) structures, a new model of porous plates, which
is called a functionally graded TPMS (FG-TPMS) plate, is investigated in this
paper. Three TPMS architectures including Primitive (P), Gyroid (G), and
wrapped package-graph (IWP) with different graded functions are presented. To
predict the mechanical responses, a new fitting technique based on a two-phase
piece-wise function is employed to evaluate the effective moduli of TPMS
structures, including elastic modulus, shear modulus, and bulk modulus. In
addition, this function corresponds to the cellular structure formulation in
the context of relative density. The separated phases of the function are
divided by the different deformation behaviors. Furthermore, another crucial
mechanical property of porous structure, i.e, Poisson's ratio, is also achieved
by a similar fitting technique. To verify the mechanical characteristics of the
FG-TPMS plate, the generalized displacement field is modeled by a seventh-order
shear deformation theory (SeSDT) and isogeometric analysis (IGA). Numerical
examples regarding static, buckling, and free vibration analyses of FG-TPMS
plates are illustrated to confirm the reliability and accuracy of the proposed
approach. Consequently, these FG-TPMS structures can provide much higher
stiffness than the same-weight isotropic plate. The greater stiffness-to-weight
ratio of these porous plates compared to the full-weight isotropic ones should
be considered the most remarkable feature. Thus, these complex porous
structures have numerous practical applications because of these high ratios
and their fabrication ability through additive manufacturing (AM) technology.Comment: 27 pages (including references), 15 figures, 12 table
Non-Uniform Rational B-Splines and Rational Bezier Triangles for Isogeometric Analysis of Structural Applications
Isogeometric Analysis (IGA) is a major advancement in computational analysis that bridges the gap between a computer-aided design (CAD) model, which is typically constructed using Non-Uniform Rational B-splines (NURBS), and a computational model that traditionally uses Lagrange polynomials to represent the geometry and solution variables. In IGA, the same shape functions that are used in CAD are employed for analysis. The direct manipulation of CAD data eliminates approximation errors that emanate from the process of converting the geometry from CAD to Finite Element Analysis (FEA). As a result, IGA allows the exact geometry to be represented at the coarsest level and maintained throughout the analysis process. While IGA was initially introduced to streamline the design and analysis process, this dissertation shows that IGA can also provide improved computational results for complex and highly nonlinear problems in structural mechanics.
This dissertation addresses various problems in structural mechanics in the context of IGA, with the use of NURBS and rational BĂ©zier triangles for the description of the parametric and physical spaces. The approaches considered here show that a number of important properties (e.g., high-order smoothness, geometric exactness, reduced number of degrees of freedom, and increased flexibility in discretization) can be achieved, leading to improved numerical solutions.
Specifically, using B-splines and a layer-based discretization, a distributed plasticity isogeometric frame model is formulated to capture the spread of plasticity in large-deformation frames. The modeling approach includes an adaptive analysis where the structure of interest is initially modeled with coarse mesh and knots are inserted based on the yielding information at the quadrature points. It is demonstrated that improvement on efficiency and convergence rates is attained.
With NURBS, an isogeometric rotation-free multi-layered plate formulation is developed based on a layerwise deformation theory. The derivation assumes a separate displacement field expansion within each layer, and considers transverse displacement component as C0-continuous at dissimilar material interfaces, which is enforced via knot repetition. The separate integration of the in-plane and through-thickness directions allows to capture the complete 3D stresses in a 2D setting. The proposed method is used to predict the behavior of advanced materials such as laminated composites, and the results show advantages in efficiency and accuracy.
To increase the flexibility in discretizing complex geometries, rational BĂ©zier triangles for domain triangulation is studied. They are further coupled with a Delaunay-based feature-preserving discretization algorithm for static bending and free vibration analysis of Kirchhoff plates. Lagrange multipliers are employed to explicitly impose high-order continuity constraints and the augmented system is solved iteratively without increasing the matrix size. The resulting discretization is geometrically exact, admits small geometric features, and constitutes C1-continuity.
The feature-preserving rational BĂ©zier triangles are further applied to smeared damage modeling of quasi-brittle materials. Due to the ability of Lagrange multipliers to raise global continuity to any desired order, the implicit fourth- and sixth-order gradient damage models are analyzed. The inclusion of higher-order terms in the nonlocal Taylor expansion improves solution accuracy. A local refinement algorithm that resolves marked regions with high resolution while keeping the resulting mesh conforming and well-conditioned is also utilized to improve efficiency. The outcome is a unified modeling framework where the feature-preserving discretization is able to capture the damage initiation and early-stage propagation, and the local refinement technique can then be applied to adaptively refine the mesh in the direction of damage propagation.PHDCivil EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147668/1/ningliu_1.pd
- …