In this paper, an efficient computational approach based on refined plate theory (RPT) including the thickness stretching effect, namely quasi-3D theory, in conjunction with isogeometric formulation ...(IGA) is proposed for the size-dependent bending, free vibration and buckling analysis of functionally graded nanoplate structures. The present novel quasi-3D theory not only possesses 4 variables as refined plate theory but also accounts for both shear deformation and stretching effect without any requirement of shear correction factors (SCFs). The size-dependent effect is taken into account by nonlocal elasticity theory. Isogeometric analysis shows a great advantage in dealing with the high continuity and high order derivative requirements of the displacement fields used in quasi-3D and nonlocal theory. The reliability and accuracy of the present method are ascertained by comparing the obtained results with other published ones. Numerical examples are also performed to show the significance of nonlocal effect, material distribution profile, aspect ratios and boundary conditions on the behaviour of FGM nanoplates.
•We present an efficient computational approach for size-dependent behaviour of FGM nanoplates.•Both shear deformation and thickness stretching effect are taken into account by a novel quasi-3D theory with only 4 variables.•Nonlocal theory that requires third order derivatives of displacement variables is used to capture the size-dependent effect.•NURBS-based isogeometric analysis can handle properly the high-order derivative requirements.•The numerical results show reliability and effectiveness of the present method.
The present investigation deals with the size-dependent analysis of the geometrically nonlinear vibration response of micro/nano-plates with and without a central cutout made of a porous functionally ...graded material (PFGM) in the presence of nonlocality and strain gradient size dependencies. In accordance with this purpose, a modified porosity-dependent power-law function is put to use to estimate the effective mechanical properties of PFGM micro/nano-plates with various porosity distribution patterns. To solve the constructed nonlinear nonlocal strain gradient problem, the non-uniform rational B-spline (NURBS)-based isogeometric analysis is utilized as an efficient discretization technique having the capability to satisfy C−1 continuity. It is seen that for specific values of the material property gradient index, porosity index and the plate deflection, the enhancement in the nonlinear frequency due to the strain gradient size effect is more than the reduction caused by the nonlocality. Furthermore, it is found that there is a specific value of the length to thickness ratio, corresponding to which the nonlocal strain gradient frequency ratio becomes minimum. This minimum value enhances by increasing the value of the porosity index of PFGM micro/nano-plates. Also, by increasing the value of the material property gradient index, the minimum point of the nonlocal strain gradient frequency ratio shifts to a higher ratio of the length to width ratio.
We present an isogeometric thin shell formulation for multi-patches based on rational splines over hierarchical T-meshes (RHT-splines). Nitsche’s method is employed to efficiently couple the patches. ...The RHT-splines have the advantages of allowing a computationally feasible local refinement, are free from linear dependence, possess high-order continuity and satisfy the partition of unity and non-negativity. In addition, the C1 continuity of the RHT-splines avoids the rotational degrees of freedom. The good performance of the present method is demonstrated by a number of numerical examples.
•We present a multi-patch isogeometric large deformation thin shell formulation based on RTH splines. It is an extension of our previous work on RHT-spline shells to large deformations and multiple patches. The coupling is based on Nitsche’s method and allows also coupling of a shell to a solid model.•Furthermore, we present a stress recovery technique to drive the adaptive h-refinement procedure in isogeometric thin structures.•The method is validated for several linear and non-linear benchmark problems including the pinched cylinder and hemispherical shell, a wind turbine rotor accounting for large deformations, a hemispherical shell with a stiffener and a pinched cylinder considering large deformations.
A phase-field description of dynamic brittle fracture Borden, Michael J.; Verhoosel, Clemens V.; Scott, Michael A. ...
Computer methods in applied mechanics and engineering,
04/2012, Letnik:
217-220
Journal Article
Recenzirano
In contrast to discrete descriptions of fracture, phase-field descriptions do not require numerical tracking of discontinuities in the displacement field. This greatly reduces implementation ...complexity. In this work, we extend a phase-field model for quasi-static brittle fracture to the dynamic case. We introduce a phase-field approximation to the Lagrangian for discrete fracture problems and derive the coupled system of equations that govern the motion of the body and evolution of the phase-field. We study the behavior of the model in one dimension and show how it influences material properties. For the temporal discretization of the equations of motion, we present both a monolithic and staggered time integration scheme. We study the behavior of the dynamic model by performing a number of two and three dimensional numerical experiments. We also introduce a local adaptive refinement strategy and study its performance in the context of locally refined T-splines. We show that the combination of the phase-field model and local adaptive refinement provides an effective method for simulating fracture in three dimensions.
We present a novel framework for topological shape optimization of curved non-conforming multi-patch and trimmed thick-shells subjected to external loads. Our method integrates the level set method ...(LSM) with a diffuse interface, a Hadamard shape derivative, and multi-patch isogeometric analysis (IGA) into a gradient descent algorithm to systematically capture the evolution of the shape. This integration enables us to directly manipulate CAD-compatible geometries and analysis techniques and to obtain the results as a CAD surface. The novelty lies in the utilization of multi-patch IGA models based on NURBS functions, which allows us to simultaneously maximize the stiffness and minimize the volume of the shell by searching for an optimal material distribution within its middle surface. The material is modeled under a small strain assumption in linear elasticity using a Reissner–Mindlin kinematic shell model in plane stress. The effectiveness of our approach is demonstrated on several curved conforming and non-conforming multi-patch geometries in 3D.
•We present a novel framework for topological shape optimization of curved thick-shells subjected to external loads.•By using multi-patch isogeometric analysis, we manipulate CAD-compatible geometries and analysis techniques to obtain the results as a CAD surface.•A NURBS-based reinterpretation of the level set method permits to obtain shapes that are directly manufacturable through additive manufacturing techniques.•The design framework offers a structure for enhancing three-dimensional parameterized shells through the utilization of compatible multi-patch Reissner–Mindlin shells.
Phase-field models based on the variational formulation for brittle fracture have recently been gaining popularity. These models have proven capable of accurately and robustly predicting complex ...crack behavior in both two and three dimensions. In this work we propose a fourth-order model for the phase-field approximation of the variational formulation for brittle fracture. We derive the thermodynamically consistent governing equations for the fourth-order phase-field model by way of a variational principle based on energy balance assumptions. The resulting model leads to higher regularity in the exact phase-field solution, which can be exploited by the smooth spline function spaces utilized in isogeometric analysis. This increased regularity improves the convergence rate of the numerical solution and opens the door to higher-order convergence rates for fracture problems. We present an analysis of our proposed theory and numerical examples that support this claim. We also demonstrate the robustness of the model in capturing complex three-dimensional crack behavior.
This study proposes a novel computationally efficient methodology to perform topology optimization (TO) of fourth-order plate structures within the framework of multi-patch isogeometric analysis. ...This is realized by taking the multifold benefits of isogeometric PHT-Splines to (1) discretize the C1 continuous weak form of plate structures, (2) develop a C0 continuous density field for the material distribution in TO and inherently remove the need for filters, and (3) provide a hierarchical tree structure for the structural mesh to effortlessly implement an adaptive mesh refinement (AMR) strategy. Moreover, to ensure continuity between isogeometric patches, we adopt a strong C1 coupling between the boundaries. This is established by constructing new basis functions, defined as a linear combination of existing C0 functions at the patch interfaces. The density field in TO is further enhanced with a first-neighbourhood smoothening algorithm based on the Shepard function to generate printable topologies and alleviate the post-processing stages after optimization. An element-centre density, based on the control point densities of the isogeometric mesh, is used as the marking scheme for the AMR to determine the subdomains to be refined. Utilizing the Geometry Independent Field approximaTion, the design and adaptive analysis-optimization stages were independently discretized respectively through NURBS and PHT-Splines, allowing easy transfer of multi-patch geometries from industry-standard packages. Multiple numerical examples illustrate the stability of the multi-patch algorithm in optimizing the geometries effectively. The results also show considerable advantages in terms of solution accuracy such as precise field, smooth topology and computational efficiency.
•Isogeometric topology optimization (ITO) for fourth-order plate structures.•Continuous material distribution to ensure smooth topology.•Boundary-tracking AMR strategy for computational efficiency.•Robust C1 coupling for seamless solution continuity across patches.•Integrating AMR into C1 coupling for ITO of multi-patch plate structures.
•An effective topology description model using the T-splines with Bézier extraction is developed.•A numerical implementation framework of the T-splines-based isogeometric analysis (T-IGA) for plate ...and shell structures with arbitrary geometries is developed.•A T-splines-oriented isogeometric topology optimization (T-ITO) method with the promising effectiveness and superior benefits is proposed.•The critical design problem of complex plate and shell structures is resolved.•Several numerical examples for plate and shell structures are studied to demonstrate the effectiveness and indispensability of the T-ITO method.
Recently, the non-uniform rational B-splines (NURBS) have been considerably employed in modeling plate and shell structures, or developing the related size, shape or topology optimization methods for their design. However, the NURBS with the tensor product feature strongly hinders the effectiveness of the optimization on complex structures. The primary intention of the current research is to propose a new T-splines-oriented Isogeometric Topology Optimization (T-ITO) method and then address the critical design problem of plate and shell structures with arbitrary shapes in practical applications. Firstly, the Bézier extraction is utilized in the T-splines to map the geometrical model into a family of Bézier elements, each of which is presented by a local Density Distribution Function (DDF) for elementary topology. A global DDF is constructed by an assembly of all local DDFs with a natural connection to the present structural topology. Secondly, the T-splines-based IsoGeometric Analysis (T-IGA) formulation with the Bézier extraction for complex plate and shell structures is developed using the Kirchhoff-Love theory, where a universal numerical implementation framework is constructed, including the Rhino, MATLAB, export modules with all geometric information and import modules for the analysis. Thirdly, a mathematical formulation for plate and shell structures with arbitrary geometries is developed using the T-ITO method to improve structural loading-capability, and the sensitivity analysis with respect to design variables is rigorously derived in detail. Finally, several numerical examples of plate and shell structures with both regular and elaborate geometries are tested to demonstrate the validity, effectiveness, superiorities and indispensability of the T-ITO method.
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