Super Finite Element Research Articles

New three-dimensional time-stepping transient fundamental solutions with applications

In this paper, alternative static-like fundamental solutions for transient dynamic analysis of three-dimensional elasticity are developed. The new formulation is based on modification of Navier's equations of elastodynamics by expressing the acceleration in terms of the displacements at different time steps using suitable finite difference scheme. The new fundamental solutions are derived via operator decoupling technique. The displacements from the previous steps are used to form the new generalized inertia terms. The new fundamental solutions are used to solve non-homogeneous media by dividing the continuous media into multi regions. The stiffness and load vector of each region are calculated using the boundary integral equation approach. Then, the whole multi-region system is solved as super finite elements. Numerical examples are solved to demonstrate the validation of the proposed solutions. The results of the proposed solutions are more stable and accurate than those of previous time domain and dual reciprocity formulations.

Vibration analysis of stiffened plates with initial geometric imperfections

This paper presents the vibration analysis of stiffened plates with initial imperfections, using both conventional and super finite element methods. Von Karman theory was utilized so as to formulate the plate element. Eccentricity of the stiffeners is also taken into account and they are not limited to be placed on nodal lines. Consequently, any configuration of plate and stiffeners can be modelled. Nonlinear finite element equations are solved using arc-length method and backbone curve is extracted accordingly. The accuracy of proposed methodology is established in comparison with previous results. Finally, the effect of geometric imperfection on vibration characteristics of stiffened plates is studied extensively.

The application of super wavelet finite element on temperature–pressure coupled field simulation of LPG tank under jet fire

Temperature–pressure coupled field analysis of liquefied petroleum gas (LPG) tank under jet fire can offer theoretical guidance for preventing the fire accidents of LPG tank, the application of super wavelet finite element on it is studied in depth. First, review of related researches on heat transfer analysis of LPG tank under fire and super wavelet are carried out. Second, basic theory of super wavelet transform is studied. Third, the temperature–pressure coupled model of gas phase and liquid LPG under jet fire is established based on the equation of state, the VOF model and the RNG k-e model. Then the super wavelet finite element formulation is constructed using the super wavelet scale function as interpolating function. Finally, the simulation is carried out, and results show that the super wavelet finite element method has higher computing precision than wavelet finite element method.

The Internal Stress Optimization of Structural Model Based on Super Finite Element Calculating Software

The structural optimization based on FE (Finite Element) software ANSYS is an emerging subject which is combines computational mechanics, mathematical programming, computer science and other engineering subject. Up to now, substantial research breakthroughs have been achieved in optimization theory. This essay is mainly about the theory analysis and internal stress optimization on the modal displayed on the contests of the Fifth National Structure Design Contest for College Student, including selection of basic components, size detail optimization of components. The optimization of structural stress is to find the optimal solutions while keep the variable within certain range. As for this paper, it is to find the optimal solution to mass while the internal stress, component size, load are under constrained. Finally, to ensure the safety of structure and component, analysis was made on the computation results.

Buckling analysis of stiffened plates subjected to non-uniform biaxial compressive loads using conventional and super finite elements

This paper presents the buckling analysis of stiffened plates, using both conventional and super finite element methods. Mindlin plate and Timoshenko beam theories are utilized so as to formulate the plate and stiffeners, respectively. The arbitrary oriented stiffeners can be positioned anywhere within the plate element and are not limited to be placed on nodal lines. Therefore, any configuration of plate and stiffeners can be modeled. Furthermore, extensive boundary conditions as well as general in-plane loading conditions can be considered using the proposed method. As the applied in-plane loads are not uniform, the buckling load is evaluated in two steps. First, the elasticity problem is solved to determine the stress distribution in prebuckling stage. Applying the principle of minimum potential energy, based on derived stress distribution, yields to the buckling equation of stiffened plates. Numerical examples are proposed to study the accuracy and efficiency of the developed super elements. Effects of various combinations of biaxial loads along with different boundary conditions on buckling characteristics of stiffened panels are also investigated.

Vibration analysis of stiffened plates using finite element method

This paper presents the vibration analysis of stiffened plates, using both conventional and super finite element methods. Mindlin plate and Timoshenko beam theories are utilized so as to formulate the plate and stiffeners, respectively. Eccentricity of the stiffeners is considered and they are not limited to be placed on nodal lines. Therefore, any configuration of plate and stiffeners can be modeled. Numerical examples are proposed to study the accuracy and convergence characteristics of the super elements. Effects of various parameters such as the boundary conditions of the plate, along with orientation, eccentricity, dimensions and number of the stiffeners on free vibration characteristics of stiffened panels are studied.

On some features of a plate hybrid-Trefftz displacement element containing a hole

The paper deals with the modelling of riveted assemblies for full-scale complete aircraft crashworthiness. To perform computations aiming at locating rupture initiation in a structure featuring more than 100,000 rivets, it is necessary to model the assembly areas using “super-elements”. If rivet elements have been developed, perforated plate super-elements are still lacking. Thus, the paper focuses on plate super-finite element formulations featuring defects, in particular holes. An original 8-node plate element containing a hole has been selected to discuss on the possibility to extend its formulation from linear (elasticity) to non-linear problems (impact). However, since little is known about the features of super-elements containing a hole, it is first attempted to clarify the properties of the selected existing super-element. This kind of element is defined according to the introduced nomenclature, and the features of its interpolation functions are highlighted. The location of stress fields computed by this super-element is proved to be in close agreement with results provided by standard FE calculations. This super-element exhibits also computational efficiency. These features encourage one to pursue the extension of this super-element formulation to large high plastic strains and strain rates, aiming at localising rupture initiation when performing crashworthiness computations of structures with many rivets and holes.

Mathematical simulation of epicycle gear vibrations in a planetary gearbox using finite element analysis

A model of forced vibrations in a planetary gearing based on the finite element and superelement method is proposed. This model is used to solve static and dynamic problems for mechanisms with planetary gearings.

Finite Element Modeling of a Membrane Sector of a Satellite Reflector Made of Triaxial Composites

Single layers of triaxial woven fabric composites have been used to make communication satellite reflectors due to their extremely light weight with good stiffness and strength property. Special superfinite elements have been developed for the analysis of these lightweight materials. These superfinite elements are used for the deflection and stress analysis of a membrane sector of the satellite reflector subjected to lateral pressure. Due to the significant difference in the size of the satellite structure (order of meters) and the size of the superfinite elements (order of millimeters) it is not possible to model the satellite structure using the superfinite elements and computer facilities available in most labs (personal computers). In the process of finding a solution to this problem, a special similitude behavior for the deflection of the curved panels made of triaxial fabrics was discovered. Using this behavior, the deflection of a large-size reflector panel (order of meters) can be analyzed using models in the millimeters size range. Stresses in the triax reflector model were also calculated. However, no special similitude behavior was obtained for the stresses.

Plane infinite analytical element and hamiltonian system

It is not convenient to solve those engineering problems defined in an infinite field by using FEM. An infinite area can be divided into a regular infinite external area and a finite internal area. The finite internal area was dealt with by the FEM and the regular infinite external area was settled in a polar coordinate. All governing equations were transformed into the Hamiltonian system. The methods of variable separation and eigenfunction expansion were used to derive the stiffness matrix of a new infinite analytical element. This new element, like a super finite element, can be combined with commonly used finite elements. The proposed method was verified by numerical case studies. The results show that the preparation work is very simple, the infinite analytical element has a high precision, and it can be used conveniently. The method can also be easily extended to a three-dimensional problem.

Impact analysis of laminated composite plates and shells by super finite elements

A super finite element method that exhibits coarse-mesh accuracy is used to predict the transient response of laminated composite plates and cylindrical shells subjected to non-penetrating impact by projectiles. The governing equations are based on the classical theories of thin laminated plates and shells taking into account the von Karman kinematics assumptions for moderately large deflections. A non-linear Hertzian-type contact law accounting for curvatures of the colliding bodies is adopted to calculate the impact force . The theoretical basis of the present finite element model is verified by analysing impact-loaded laminated composite plate and shell structures that have previously been studied through analytical or other numerical procedures. The predictive capability of the present numerical approach is successfully demonstrated through comparisons between experimentally-measured and computed force-time histories for impact of carbon fibre-reinforced plastic (CFRP) plates. The current computational model offers a relatively simple and efficient means of predicting the structural impact response of laminated composite plates and shells.

Nonlinear analysis of orthogonally stiffened cylindrical shells by a super element approach

The super finite element method is extended to the nonlinear static and dynamic analysis of orthogonally stiffened cylindrical shells. Both geometric and material nonlinearities are included and the temporal equations are solved by the implicit Newmark-β method with Newton-Raphson subiterations. The new formulation has been tested in various applications and a few illustrative examples are presented.

Vibration Analysis of Orthogonally Stiffened Cylindrical Shells Using Super Finite Elements

An efficient numerical technique for the free vibration analysis of orthogonally stiffened cylindrical shell structures is presented. The new technique is developed within the framework of a super finite element method and involves formulation of C1 cylindrical shell and curved beam elements. The displacement functions used in the present formulation combine the usual polynomials with some analytical functions, carefully chosen to provide a good approximation of basic vibration modes in conjunction with coarse grid modelling strategy. Detailed results of vibration application of these elements are presented.

New design-analysis techniques for blast loaded stiffened box and cylindrical shell structures

This paper presents a brief review of some new design-analysis techniques for blast loaded engineering structures. The super finite element method, previously developed for stiffened plates, has been extended to more complex and larger structures such as orthogonally stiffened rectangular boxes and cylindrical shells. Both geometric and material nonlinearities are included in the modelling. The mathematical formulation of the new super elements is briefly outlined and some illustrative examples are presented.

Non‐linear analysis of stiffened plates using super elements

AbstractA new numerical technique for large deflection elasto‐plastic analysis of stiffened plates is presented. The method uses super finite elements which are macro elements having analytical as well as the usual finite element shape functions, specially designed so that only one plate element per bay and one beam element per span are needed. The large deflection theory by von Karman and the von Mises yield criterion and associated flow rule are employed. The governing equations are derived using the principle of virtual work, integrated numerically using Gauss quadrature and solved by Newton–Raphson iteration. Numerical solutions are presented for simple beams and plates, and plates stiffened in one or two mutually perpendicular directions. Good approximations are obtained with only one‐element representations of each plate bay or beam span with significant savings in computing time, costs and storage requirements as compared with using regular finite elements.

A versatile panel element for the analysis of shear wall structures

A panel element substructure is developed, defined in terms of boundary node arrangement and intended for use in efficient static and dynamic analysis of shear wall and box-type structures. The panel substructuring scheme is described as a multi-level super finite element technique based on a series of static condensations. A stressdisplacement matrix, compatible with the reduced representation of panel stiffness and mass, allows full stress recovery within the element. A catalogue of element formations is created to allow selection of the desired substructure nodal arrangement with a minimum of computer input compared to the corresponding fully assembled finite element model. Several numerical examples are presented to demonstrate the versatility and accuracy of the panel elements when used for either static or dynamic analysis.

Anisotropic Hybrid Displacement Singularity Element

The displacement-hybrid method of finite element formulation is extended to the development of a singularity super finite element which can be used to model the behavior of a sharp crack in a rectilinearly anisotropic plane. Functional representations of the displacement field surrounding a sharp crack in a rectilinearly anisotropic plane are developed from the planar form of the linear theory of anisotropic elasticity. The formulation of the displacement-hybrid singularity super element is based on a variational principle obtained from a generalization of the total potential energy. The displacement-hybrid model singularity element which results from the formulation possesses boundary and interior displacement fields which are distinctly different in nature. Certain available numerical results, which tend to confirm the validity of the formulation, are presented.