Propeller Stress Calculation Using Curved Finite Element

This paper presents a zeroth-order (non-gradient based) methodology for topology optimization of continuum structures. The solid and void elements in the design domain are represented by binary design variables. As in the SIMP method, design variables are assumed to represent the non-dimensional density of the individual finite elements and their contribution to structural stiffness in the model. The optimization procedure begins by specifying a desired volume fraction over a discretized domain and associated boundary conditions. Based on a randomized distribution of solid and void elements, a finite element analysis is performed to identify the strain energy of individual elements. While keeping the volume fraction fixed, the solid elements with low strain energy are converted into void elements whereas the void elements with high strain energy are converted into solid elements. The strain energy threshold for element exchange is specified at the beginning and can be adjusted in the course of optimization. Through subsequent repetition of analysis and exchange steps, the optimal topology corresponding to minimum compliance emerges with no gray elements to filter out. The general characteristics of the Element Exchange Method are demonstrated through solutions of several benchmark problems.

This study is focusing on the finite element simulation of low velocity impact applied to glass fiber-reinforced composites. Elasto-visco-plasticity is adopted taking into account strain rate effect, with isotropic hardening. To avoid numerical locking, hexahedral solid shell finite element SS is developed. The formulation is based on the mixed Assumed Natural Strain (ANS) and the Enhanced Assumed Strain (EAS) methods. A geometrical non linear condition is applied. The finite element is implemented in UEL subroutine via the commercial software ABAQUS/Standard. The numerical element proved its efficiency comparing to conventional element and previous experimental results in (Mars et al. 2018). Numerical simulations with solid element are conducted using Abaqus/standard via user material UMAT subroutine. In terms of computation time, the solid shell element is less time consuming when comparing to conventional solid element. This is due to the fact that a single element through the thickness direction is adopted. Element efficiency is assessed for various fibers contents.

Piezocomposites are attracting widespread interest since they can offer greater flexibility and better performances in specific applications with respect to traditional piezoelectric wafers. Design of piezocomposites requires accurate homogenisation models for the prediction of the equivalent electro-mechanical properties. In macro-scale models of structures with piezocomposite transducers, these properties are adopted in order to avoid the complexity of the piezocomposite microstructure. In the case of smart structures the accurate modelling of the actuation and the response of the structure is of primary importance. If classical structural finite elements are not sufficiently accurate, higher order or solid elements should be adopted. Thanks to adaptation or mixed-dimensional methods, it is possible to adopt computationally expensive higher order or solid elements only in some sub-domains of the structure. In this work, the modelling of smart structures equipped with thin piezoelectric transducers is considered in a multi-scale framework. Micromechanical homogenisation models are developed and employed for the prediction of the equivalent properties of piezocomposites. A micromechanical model based on the concept of inclusion is proposed to investigate the influence of the shape of the inclusions, of the constituent materials and of the polarisation on the equivalent properties. It has been found that fibre-shaped inclusions should be considered in order to obtain piezocomposites with strong piezoelectric effect and to have at the same time high direction-dependence. The equivalent properties of Macro Fiber Composites are determined via the Asymptotic Homogenisation Method (AHM) with an analytical solution and with a numerical solution via FEM which takes into account the effect of the electrodes. AHM analytical solution is adopted to investigate the effect of the material properties of the matrix on the overall piezocomposite. Results indicate that low values of the Young's modulus and of the Poisson's ratio yield high directional dependence in the piezoelectric properties. A laminated design with anisotropic layers and a piezocomposite layer is investigated via UFM. A configuration with maximum directional dependence in terms of equivalent piezoelectric strain constants is proposed, whereas maximum directional dependence in terms of piezoelectric stress constants is proved to be not achievable with such a design. Hierarchical finite elements for structural analyses based on a Unified Formulation (UF) by Carrera are developed and coupled via the Arlequin method proposed by Ben Dhia. Solid, plate and beam finite elements for mechanical and for piezoelectric problems are presented. Via UF, higher order and piezoelectric elements can be formulated straightforwardly. These elements are combined in variable kinematic solutions in the Arlequin framework. Higher-order elements are adopted locally where the stress field is three-dimensional, whereas the remaining parts of the structure are modelled with computationally cheap lower-order elements. Two electro-mechanical coupling operator for the Arlequin method in the context of piezoelectric analyses are proposed. Results are validated towards monomodel solutions and three-dimensional analytical and numerical reference solutions. Accurate solutions are obtained reducing the computational costs

A finite element post-processor for fatigue assessment of welded structures based on the Master S-N curve method

A rational approach to the general solution of the propeller strength problem is established. A finite-element displacement model is utilized to predict the behavior of an elastic body having an arbitrary shape and subjected to prescribed loading. Solid elements in their general form are adopted. This formulation bypasses the constraints of simplified assumptions commonly employed by many classical plate and shell theories, and allows a more realistic approximation to the true structural configuration than is possible by most other conventional approaches. The application of the present procedure is simple and straight-forward. Good agreements with measured displacements and experimental stress data were obtained for a highly skewed blade as well as a supercavitating blade.

This paper presents a multi-dimensional variable-kinematics finite element model for nonlinear static analyses of structures with complex geometries. The approach incorporates higher-order beam models and classical solid finite elements in a unified framework, enabling refined modeling of complex geometries. The finite element procedure proposed follows the Carrera Unified Formulation (CUF) and uses a pure displacement-based methodology. The governing equations are derived within the classical continuum mechanics framework, and weak-form equilibrium equations are established using the Principle of Virtual Displacements (PVD). Within the CUF framework, higher-order beam and hexahedral solid models are defined in a unified manner, and the governing equations are written in terms of invariants of mathematical models used and the theory of structures approximation. A coupling technique is used between the beam and solid elements at the nodal level using superposition. The capabilities of fully nonlinear variable-kinematics models are investigated for the static analysis of various rectangular and curved structures. The numerical results are compared with solutions obtained using commercial software. Finally, the proposed methodology is applied to analyze more complex geometries in engineering applications. The results show the capabilities of variable-kinematics models in terms of both accuracy and computational efficiency for the computation of highly nonlinear deformed states and localized phenomena, such as stress concentrations and buckling.

In this paper, the structure of cylindrical shell with a reinforced circular cutout using combination model of solid element and shell element was analyzed by Finite Element Method (FEM) simulations. Multipoint constraint (MPC) method is mainly used to solve the connection between solid element and shell element when considering the calculation accuracy and efficiency of the model. The combination model of solid and shell element is established in ANSYS, and has been compared to the model of shell element and the model of solid element. The result showed that in the aspects of the stress distribution of the pressure hull near the cutout, buckling behavior of the structure and its instability response, the combination model of solid and shell element was almost equal to the others, it is convincible as well as possessing merits of other models.

This is the first of a two part paper on three‐dimensional finite elements with rotational degrees of freedom (DOF). Part I introduces an 8‐node solid hexahedron element having three translational and three rotational DOF per node. The corner rotations are introduced by transformation of the midside translational DOF of a 20‐node hexahedron element. The new element produces a much smaller effective band width of the global system equations than does the 20‐node hexahedron element having midside nodes.A small penalty stiffness is introduced to augment the usual element stiffness so that no spurious zero energy modes are present. The new element passes the patch test and demonstrates greatly improved performance over elements of identical shape but having only translational DOF at the corner nodes.

A finite element formulation is developed including the fully coupled electrical-structural constitutive relations. An effort has been made to develop the most general formulation applicable to laminated composite plates with inclusion of piezoceramic sensors/actuators. To this end, the von Karman large deflection theory was included, due to the results obtained from the experiments conducted. Solution of the large deflection problem lead to an electrical-structural coupled tangent stiffness, which is believed to be the first time reported in the literature. paper presents comparison of the finite element simulation to experimental results for both static and dynamic piezoceramic sensors in addition to dynamic piezoceramic actuation. INTRODUCTION Piezoelectric material maintains a complex and intricate relationship between several physical sciences such as materials, thermal, electric fields, and elasticity. Evidence of the piezoelectric's complexity can be demonstrated by the seemingly continuous research conducted since its discovery in 1880 by Pierre and Jaques Curie. Much of the research set out to determine analytical models describing the piezoelectric phenomenon and lead to discrete devices such as extremely sharp crystal filters and stable oscillators. Mindlin developed classical methods describing the analysis on waves and vibrations in isotropic elastic plates concurrently with high frequency vibration of crystal plates. Allik and Hughes developed a solid, or three dimensional, finite element to model transducers and crystal oscillators. However, given that smart structures typically consist of thin piezoelectric layers attached to structures that are several orders of magnitude greater in thickness, the solid finite element formulation leads to an inherently inefficient process in which to model the complete physical structure. Subsequently Tzou and Tseng * Graduate Student, Student member AIAA. t Professor, Associate Fellow AIAA. This paper is declared a work of the U.S. Government and is not subject to copy right protection in the United States. formulated a new thin piezoelectric solid finite element in the form of shell and plate elements. When considering piezoelectrics in conjunction with structural members, linear piezoelectric theory simplifies the piezoelectric effect. Linear piezoelectric theory assumes an isothermal adiabatic process and quasi-static electric field equations. research presents a comparison of the fully coupled electricalstructural finite element analysis of an isotropic panel with a surface mounted piezoelectric patch to experimental results. PIEZOELECTRIC RELATIONS Piezoelectric material inherently possesses coupling between electrostatics and structural dynamics. Linear piezoelectric theory yields an intrinsically coupled pair of piezoelectric constitutive equations. One describes the direct piezoelectric effect where the state of strain gives rise to an electric polarization, and the other describes the converse effect where an applied electrical field develops a state of strain. For a thin piezoelectric layer, the following constitutive relations result from linear piezoelectric theory (1)

In order to propose a simplified simulation method using finite element (FE) model for predicting deformation and residual stress generated by multi-pass butt welding, a series of experiments and numerical analyses were carried out. 3-pass butt welding of steel plates was simulated by the thermal elasto-plastic analysis with shell elements and with solid elements respectively. A heat input model for considering the temperature distribution in the thickness direction in shell elements was proposed. The validity of the heat input model was verified by comparing analytical results with experimental results or other analytical results using solid elements. Furthermore, the effectiveness for saving computing time by using shell elements was confirmed from the comparison with the case using solid elements. It was confirmed that the welding out-of-plane deformation and residual stress could be predicted with high accuracy by the proposed method. The computing time was around 14% of that by the precise model with solid elements.

An efficient multiphysics solid shell based finite element approach for modeling thin sheet metal forming processes

The objective of this study was to construct a finite element model of a golf ball and an impact simulation model between the ball and a club, and to devise a method for the construction of simulation models by investigating the factors affecting the behaviour of the ball during and after impact. A ball model with hyperelasticity and viscoelasticity was constructed using solid elements, and the relationship between the material properties and the ball behaviour at impact was revealed by varying several material constants of the ball model. A finite element model of a club with elasticity was created from a computer-aided design surface model of a commercially available driver. The club head and shaft were modelled using solid and shell elements, respectively. The effects of initial conditions at impact on the rebound behaviour of the ball, that is, the velocity, angle and spin rate, were investigated from impact simulations by varying the impact points of the ball and the postures of the club. Then, methods for the construction of simulation models were proposed based on these relationships. Impact experiments were also conducted to obtain the ball behaviour. The results simulated using the models, constructed by the proposed methods, closely matched the experimental results.

ABSTRACT: The goal of this paper is to present recent developments aimed at improving computational efficiency and extending the range of material applicability of a 2D/3D FDEM geomechanical simulation software. Firstly, a hybrid FEM-FDEM logic was devised to allow for user-defined regions of the domain to be modeled as a continuum, while the remainder is captured by the FDEM formulation with an intrinsic cohesive zone model explicitly capturing fracturing. Benchmarking results indicate simulation speed-ups of up to 48x when using the new logic versus the traditional full FDEM approach. Secondly, the finite element formulation was enhanced with elasto-plastic constitutive models based on Drucker-Prager and Mohr-Coulomb failure criteria, effectively broadening the range of applicability to materials that exhibit irreversible damage processes under load without breaking. These developments were initially verified by comparing simulated stress distributions against analytical solutions for select boundary value problems. Practical validation of the novel FDEM formulation was achieved by capturing the variation of critical failure mechanism observed in a slope as a function of the type of rock mass jointing. The factors of safety computed with the strength reduction method compared very well with those reported in the literature for commercially available programs based on DEM and FEM. Finally, a direct comparison between FEM-based, elasto-plastic and FDEM-based, brittle-fracture models is presented for the case of a homogeneous rock slope. 1. INTRODUCTION The finite-discrete element method (FDEM) is a numerical method originally introduced by Munjiza et al. (1995) as a means of combining principles of continuum mechanics, such as the theory of elasticity and non-linear fracture mechanics, with discrete element algorithms to model fracture, fragmentation, and failure of cementitious materials and rocks. Building upon Munjiza's pioneering work, FDEM has been further developed by a multitude of research groups and organizations worldwide, and applied to a variety of rock mechanics and rock engineering problems where consideration of brittle fracturing processes is critical. Over the years, developments of FDEM have focused on several major areas of interest including (i) improvement of the core algorithms for deformation, fracture, interaction, and contact detection (e.g., Lei et al., 2016, Fukuda et al., 2021, Cai et al., 2023), (ii) incorporation of multi-physics capabilities to account for hydraulic and thermal effects (e.g., Yan and Jiao, 2018, Yan et al., 2019, Munjiza et al., 2020), and (iii) reduction of simulation run times by parallel computing (e.g., Lei et al., 2014; Lisjak et al., 2018; Fukuda et al, 2019). In the classic implementation of FDEM (Munjiza, 2004), the numerical representation of fractures is achieved by an intrinsic cohesive zone model (ICZM). With this approach, zero-thickness cohesive crack elements are inserted (at the beginning of the simulation) across pairs of adjacent solid finite elements throughout the entire modelling domain. All irreversible ("plastic") deformations are concentrated in the form of yielding and breakage of the interfaces between the solid finite elements, which remain elastic.

Modern software packages for calculating buildings and structures for various types of action make it possible to simulate the structure and its elements in sufficient detail and to reflect adequately the behavior of this structure. However, detailed simulation with the use of solid finite elements requires a large amount of computing time to perform calculations. This problem can be solved by moving from solid finite elements to bar elements. At the same time, it is necessary to verify the bar calculation models. The article compares the calculation results of a reinforced concrete column simulated in two ways: with the use of solid finite elements based on the actual reinforcement and with the use of bar finite elements. The concrete material for the reference model is specified using a Continuous Surface Cap Model nonlinear model implemented in the LS-DYNA software package. This model reflects the non-linear behavior of concrete and enables to consider the joint behavior of concrete and reinforcing bars. The diagrams of concrete behavior in the bar model are adopted in accordance with SP 63.13330.2012 “Concrete and reinforced concrete structures. Revised edition of SP 52-101-2003”. The study compares the results obtained by the breaking load value and the fracture pattern of the column under consideration.

Finite element analysis of composite structures with smart constrained layer damping