Experimental and Numerical Investigation of Contact Parameters in a Dovetail Type of Blade Root Joints

this paper focuses on the contact characteristics of the blade root joints subjected to the dry friction damping under periodic excitation. The numerical method and experimental procedure are combined to trace the contact behavior in the nonlinear vibration conditions. In experimental procedure, a novel excitation method alongside the accurate measurements is used to determine the frequencies of the blade under different axial loads. In numerical simulations, local behavior of contact areas is investigated using the reduction method as a reliable and fast solver. Subsequently, by using both experimental measurements and numerical outcomes in a developed code, the global stiffness matrix is calculated. This leads to find the normal and tangential stiffness in the contact areas of a dovetail blade root joints. The results indicate that the proposed method can provide an accurate quantitative assessment for investigation the dynamic response of the joints with focusing the contact areas.

Determination of Transverse Shear Stiffness of Sandwich Panels with a Corrugated Core by Numerical Homogenization

Knowing the material properties of individual layers of the corrugated plate structures and the geometry of its cross-section, the effective material parameters of the equivalent plate can be calculated. This can be problematic, especially if the transverse shear stiffness is also necessary for the correct description of the equivalent plate performance. In this work, the method proposed by Biancolini is extended to include the possibility of determining, apart from the tensile and flexural stiffnesses, also the transverse shear stiffness of the homogenized corrugated board. The method is based on the strain energy equivalence between the full numerical 3D model of the corrugated board and its Reissner-Mindlin flat plate representation. Shell finite elements were used in this study to accurately reflect the geometry of the corrugated board. In the method presented here, the finite element method is only used to compose the initial global stiffness matrix, which is then condensed and directly used in the homogenization procedure. The stability of the proposed method was tested for different variants of the selected representative volume elements. The obtained results are consistent with other technique already presented in the literature.

Parallelized Element-by-Element Solver for Structural Analysis of Flexible Pipes Using Finite Macroelements

Due to the number of layers and their respective geometrical complexities, finite element analyzes of flexible pipes usually require large-scale schemes, with a high number of elements and degrees-of-freedom. If proper precautions are not taken, such as suitable algorithms and numerical methods, the computational costs of these analyzes may become unfeasible to the current computational standards. Finite macroelements are finite elements formulated for the solution of a specific problem considering and taking advantage of its particularities, such as geometry patterns, in order to obtain computational advantages, as reduced number of degrees-of-freedom and ease of problem description. The element-by-element method (EBE) also fits very well in this context, since it is characterized by the elimination of the global stiffness matrix and its memory consumption grows linearly with the number of elements, besides being highly parallelizable. Over the last decades, several works regarding the EBE method were published in the literature, but none of them directly applied to flexible pipes. Due to the contact elements between the layers, problems with flexible pipes are usually characterized by very large matrix-bandwidth, making the implementation of EBE method more challenging, so that its efficiency and scalability are not compromised. Therefore, this work presents a parallelized implementation of an element-by-element architecture for structural analysis of flexible pipes using finite macroelements, consisting of an extension of a previous work from the same authors. New synchronization algorithms were developed, with scalability improvements, the methodology was extended to other finite macroelements and comparisons were made with a well-stablished FEM software, with significant gains in simulation time and memory consumption.

Full-Space Response Surface Method for Analysis of Structural Reliability

In order to improve the computational efficiency of the response surface method (RSM) in analysis of structural reliability, a full-space response surface method (FRSM) is presented in this paper. First, a vector-type response surface is developed by expanding the stochastic nodal displacement vector along the Krylov basis vectors defined by the global stiffness matrix and the force vector. Then the effective collocation points are picked out of the candidate ones according to the linear independence of the combining row vector. Finally, the unknown coefficients of the proposed response surface are determined by means of the regression analysis. Examples show that the proposed FRSM requires much fewer effective collocation points and less times of finite element analysis, achieving much higher computational efficiency by comparing with the traditional RSM.

Analysis of Key Elements of Truss Structures Based on the Tangent Stiffness Method

In recent years, the topic of progressive structural collapse has received more attention around the world, and the study of element importance is the key to studying progressive collapse resistance. However, there are many elements in truss structures, making it difficult to predict their importance. The global stiffness matrix contains the specific information of the structure and singularity of the matrix can reflect the safety status of the structure, so it is useful to evaluate the key elements based on the global stiffness matrix for truss structures. In this paper, according to the tangent stiffness-based method for the element importance, the square pyramid grid was chosen as an example, and the distribution rules of key elements under different support conditions, stiffness distributions, and geometric parameters were studied. Then, three common symmetric grid forms, i.e., diagonal square pyramid grids, biorthogonal lattice grids, and biorthogonal diagonal lattice grids, were selected to investigate their importance indices of elements. The principle in this work can be utilized in progressive collapse analysis and safety assessment for spatial truss structures.

Mechanical properties of hexagonal boron nitride monolayers: Finite element and analytical predictions

The mechanical response of two-dimensional nanostructures may be significantly affected by their size. In this work, a molecular structural mechanics model is developed and is implemented in order to predict the nanomechanical behavior and calculate the corresponding elastic properties of hexagonal boron nitride sheets and describe their size-dependence. The finite element approach utilizes appropriate spring-like elements for the modeling of interactions between atoms within the hexagonal boron nitride structure, the stiffness constants of which are obtained by the molecular mechanics theory. Adopting conventional finite element techniques, the global stiffness matrix of the structure of a desired sheet size can be assembled. Applying appropriate boundary conditions, the governing equilibrium static equation can be solved and the elastic mechanical properties as Young’s modulus, shear modulus, and Poisson’s ratio of the structure can be calculated. Fitting the results of the mechanical properties calculated by the finite element analysis, analytical–empirical equations are proposed for their direct prediction for an hexagonal boron nitride sheet having the size parameters of the structure as independent variables.

Application of Craig-Bampton Reduction Technique and 2D Dynamic Infinite Element Modeling Approach to Membrane Vibration Problems

ABSTRACTAn approach is presented for solving membrane vibration problems using an integrated scheme consisting of the Craig-Bampton (CB) reduction technique and a 2D dynamic infinite element modeling (DIEM) method. In the proposed CB-DIEM scheme, the substructure domain is partitioned into multiple layers of geometrically-similar infinite elements (IEs) which use only the data of the boundary nodes. A convergence criterion based on the first invariant of the DIEM mass matrix is used to determine the optimal parameters of the CB-DIEM scheme, namely the proportionality ratio and number of layers in the DIEM partitioning process and the number of retained frequency modes in the CB reduction method. Furthermore, in implementing the CB method, the inversion of the global stiffness matrix is calculated using only the stiffness matrix of the first element layer. Having reduced the DIEM model, a coupled DIE-FE algorithm is employed to model the dynamic problems of the full structure, which removes the respective methods disadvantages while keeping their advantages. The validity and performance of the proposed CB-DIEM method are investigated by means of three illustrative problems.

Flutter Instability of Cracked Rotating Non-Uniform Beams Subjected to Distributed Follower Force

In this paper, the effect of an open edge crack on the instability of rotating non-uniform beams subjected to uniform distributed tangential compressive load is studied. The local stiffness due to the presence of crack is considered in the global stiffness matrix of the structure using the finite element method. The cracked beam element is modeled as two equal sub-beam elements connected by a massless rotational spring. Based on the fracture mechanics, the strain energy release rate and the stress intensity factors are employed to investigate the stiffness of the rotational spring. Then, the modified shape functions are developed to reflect the crack stiffness in the finite element analysis. To validate the accuracy of the finite element model and results obtained, comparisons have been made between the results obtained and those available in the literature. The effects of several parameters, including the linear and nonlinear thickness variations, angular velocity, crack location and size, on the instability of cracked rotating non-uniform cantilevers are also examined. The results show that the location of crack significantly influences the critical magnitude of the follower force that destabilizes the cantilevers. In addition, geometric non-uniformity reduces the stability of the cracked cantilevers. For the same amount of cantilever mass, different patterns of mass distribution result in different stability diagrams.

Static and Dynamic Analysis of Cracked Concrete Beams Using Experimental Study and Finite Element Analysis

In this paper, a simple method for defining the effects of cracks on elastic behavior of beam is presented. The cracked sections were modelled as rotational springs and the problem was solved using the finite element method. The global stiffness matrix of a beam with multiply cracked section was then assembled. For calculation of rotational spring stiffness equivalent to uncracked and cracked sections, finite element models and experimental test were used.The natural frequencies and mode shape of beams with multiple single-edge cracks were obtained and a new simple formula was proposed. Published numerical examples for cracked beams were used for validation.