Flat Finite Element Research Articles

Modeling and calculation of panel buildings made of cross-laminated timber

Buildings made using cross-laminated timber have become widespread over the last decade. The experience of designing and operating such buildings of various functional purposes confirms the expediency of their construction and use. This article provides a solution to the problem of modeling and calculating panel houses made of cross-laminated timber using the finite element method using the given mechanical characteristics of the material. The possibility of modeling and calculating panel buildings made of cross-laminated timber using the finite element method with the use of flat finite elements, taking into account the orthotropic properties of the material, under the condition of using the reduced modulus of elasticity according to the previously proposed method and adjusting Poisson's coefficients, in such a way as to maintain the condition of existence of elastic potential. The algorithm for modeling panel buildings made of cross-laminated timber using the finite element method as a system "soil base-foundation-above-ground structure system" is given.

Determination of the survivability parameters of a reinforced concrete spatial frame operating under conditions of a complex stress state

The calculation for stability against progressive collapse in a dynamic setting, regulated by the norms, contains general recommendations on the possibility of taking into account a pliable foundation and including non-load-bearing elements in the calculation model without determining the limits of their applicability. The results of experimental studies and numerical analysis of a reinforced concrete experimental design of a spatial frame - a fragment of the frame of a multi-storey building in limiting and transcendental states are compared. The features of deformation of the structural system before and after the beyond-design impact, which causes its sudden structural restructuring, are established. Numerical studies were performed with and without considering the pliable foundation, as well as including or not including non-load-bearing elements in the calculation. Satisfactory agreement between the data of experimental studies and the results of dynamic calculation has been obtained. As one of the variants of the calculation model, a modified scheme was adopted, the constituent part of which are the elements of the calculation model of the second level - a fragment of the frame, modeled by volumetric and flat finite elements. It has been established that the results of the dynamic calculation of the experimental fragment are consistent with the experimental data only when taking into account the elements of the load device and real boundary conditions, including the deformable base.

ТРЕУГОЛЬНЫЙ КОНЕЧНЫЙ ЭЛЕМЕНТ С ШЕСТЬЮ СТЕПЕНЯМИ СВОБОДЫ В УЗЛЕ

The work is devoted to obtaining the stiffness matrix of a high-precision, flat finite element with 6 degrees of freedom in the node, for solving plane elasticity problems by the finite element method.
 The scientific literature describes higher order elements. However, the theoretical results of these studies are quite far from their practical application. This paper gives a very detailed derivation of the stiffness matrix of a high-precision finite element. Similarly, a stiffness matrix of a tetrahedral finite element with 12-degree-of-freedom node can be obtained. To test the obtained stiffness matrix, a program based on the FEM was written, with the help of which the cantilever beam is calculated. The error in calculating displacements is only 0.22%.
 Conclusion: the stiffness matrix presented in the paper can be used with great success in numerical methods for calculating the stress-strain state.

Method of calculation of panel buildings from cross-laminated timber

Building constructions made of cross-laminated timber become more and more widespread. Experience in the timber structures design and operation for various purposes confirms the feasibility of their use. Recently, the construction of prefabricated cross-laminated timber houses has become especially widespread. The problem solution of cross-laminated timber panels calculation by means of a finite element method with the material`s reduced mechanical characteristics application is offered in this article. The specified formulas for definition of the reduced geometrical and mechanical characteristics of cross-laminated timber panels` various types, including those made of combined cross-laminated timber, are resulted. The algorithm of cross-laminated timber panels calculation by means of a finite element method is resulted. The possibility of using flat finite elements taking into account orthotropic properties for the calculation of cross-laminated timber panels using the elasticity above modulus according to the above method, adjusting the Poisson's ratios so as to preserve the condition of elastic potential in timber, is reasoned.

Methods to Reduce Material Intensity of Tail Sections of Launch Vehicles

A technique has been developed for reducing the material intensity of highly stressed tail sections of launch vehicles, taking into account strength and stability constraints as well as technological requirements. A cylindrical longitudinally and transversely ribbed waffle-grid (lattice) shell with rectangular holes is taken as the design scheme of the tail section, with its lower end being fastened at locations of support brackets, and the upper one being loaded with longitudinal compressive forces, evenly distributed along the contour, due to the action of the weight of higher-located structure elements. The optimization algorithm is based on the principle of ensuring discrete uniform strength of individual elements (substructures). The structural geometric dimensions of cross-sections of a standard tail section and the stiffness parameters of longitudinal and transverse load-bearing frames, the wall thicknesses of shell elements, the dimensions of lattice shells, etc., are selected from the requirements of stress-strength reliability: constraints on the limiting values of equivalent stresses (strength conditions), compressive stresses of the local and general buckling, and a number of design and technological requirements. The direct calculation of the tail section and the search for its variable geometric parameters are proposed to be performed using an interactive numerical-analytical (finite element method – engineering analysis) algorithm. The initial calculation of the static stress-strain state of the lattice-reinforced tail section was carried out by the finite element method, which is implemented in the NASTRAN package. To discretize the shell and its ribbing, flat finite elements were used. In the process of the finite-element numerical modeling of the tail section state, the reliability of the obtained results of calculating the equivalent stresses was analyzed by studying the convergence of the results of calculations on a series of meshes with different refinement. Results of the application of the developed technique to reduce the mass of the standard tail section of the Antares launch vehicle are presented.

Analysis the results of calculating the monolithic wall in the soil with anchor fastening without distribution beams based on the solution the spatial problem with various topology the element of fencing

The article analyzed the results of the calculation of the monolithic trench “wall in soil” (WIS) with fastening attachment anchors without the use of distribution beams based on solving a spatial problem with the different topology of the fence elements. In practice, when solving such problems in a flat arrangement, it is assumed that the WIS is a solid construction in the longitudinal direction, vertical concreting joints are not taken into account, formed between grabs, rupture along horizontal longitudinal reinforcement between adjacent spatial frames, reduction of the rigidity of the WIS structure due to the formation and opening cracks in two directions, as well as inelastic operation of the compressed zone concrete. Analysis of stress-strain state (SSS) of the fence construction structure based on the results of spatial calculation with different topology (flat and volumetric) of finite elements (FE) showed the need to correct the calculation methodology. Based on the results of the calculations, it was found that the values of internal forces in the design obtained using flat FE are significantly overestimated. Based on the numerical method of studies, recommendations on the selection of the design scheme of the monolithic reinforced concrete structure of the pit’s fence are proposed and the calculation methodology is corrected. The subject of the study, the results of which are presented in this article, was the specifics of the operation and calculation of the WIS with anchor attachment without distribution beams and the analysis of the calculation results based on the solution of the spatial problem with different topology (flat and volume) of the FE structure of the fence.

Інженерна методика розрахунку елементів із комбінованої клеєної деревини

Extensive world experience in the implementation of building structures made of timber, in particular glued timber, for various purposes confirms the feasibility of their use. This is facilitated by the fact that glued timber effectively accumulates the positive properties of timber as a structural material level the shortcomings of solid timber. One of the types of constructions of glued timber are constructions of combined glued timber. Taking into account the structure and features of elements of combined glued timber of rectangular cross section, for a detailed analysis of the stress-strain state, a method is proposed, which consists in applying to standard formulas for calculating the reduced cross-sectional characteristics: reduced area, reduced moment of inertia, reduced moment of resistance. To calculation, the elements of combined glued timber of rectangular cross section according to the second limit state (serviceability), it is proposed to use the reduced modulus of elasticity of the section to the boards of the outer layers. To analyze the proposed method, a number of numerical studies of beams of combined and glued timber of the same strength class using analytical calculation methods and using the finite element method in the software package LIRA-CAD, using three-dimensional and flat finite elements. Numerical studies show that the results of calculations of beams of combined glued and glued timber of the same strength class differ within 20% in the direction of increasing the values of deflections and normal stresses in the elements of combined glued timber. Finite element calculations in the software package LIRA-CAD beams of combined and glued timber of the same strength class modeled volumetric and flat showed almost complete coincidence of results with a discrepancy of up to 2%, which suggests the need to significantly simplify the modeling, set elements from glued timber with flat finite elements. It is confirmed that the analytical calculation of beams of combined glued timber is recommended to be carried out according to the proposed method. The proposed technique allows to take into account the thickness and mechanical characteristics for the strength class of each board of which the glued cross section of the element, which significantly expands the range of use of combined glued timber. The high level of coincidence (within 5%) of the proposed analytical method with determination of the given cross-sectional characteristics with the results obtained by the finite element method for different cross-sections and spans of beams is confirmed, which allows to assert the expediency of its application in engineering calculations. In addition, the modeling of structures made of combined glued timber is possible with rod elements with the provision of the reduced modulus of elasticity according to the proposed method, which greatly simplifies the calculation of complex rod systems.

Verification Analysis of the Degradation of Frequency Parameters Under the Action of Seismic Load

The article discusses the results of a numerical study of the effect of local damage to bearing structures on the degradation of frequency parameters during seismic effects. The studies were carried out in the LS-DYNA software package which implemented the nonlinear concrete model — Continuous Surface Cap Model (CSCM). Design models of a building are modelled both with regard to direct reinforcement using volumetric FE (finite elements) and flat FE. The object of modelling is a 3-storey building of cellular framing. The analysis of the results of the conducted studies suggests that the effect of degradation of natural vibration frequencies cannot be estimated in the building modelled by means of bar FE. The degradation is insignificant; the frequency reduction occurs within the limits of errors. At the moment, it is not possible to identify the effect of degradation in the bar model in this formulation. To do this, it is necessary to conduct additional researches, including those with other models of materials. Taking into account certain assumptions, the LS-DYNA software package allows computational studies of the effect of local damage to bearing structures on dynamic characteristics, including those resulting from an earthquake.

Tria and quad plate finite elements based on RZT(m) for the analysis of multilayered sandwich structures

Aim of the paper is to develop and to assess a class of plate finite elements for the analysis of multilayered composite and sandwich structures. The adopted model is the mixed Refined Zigzag Theory (RZT(m)), based on the kinematics of the Refined Zigzag Theory (RZT) and on the assumption of transverse shear stresses coming from integration of indefinite equilibrium equations. A triangular and quadrilateral flat finite element are developed by means of the Reissner’s Mixed Variational Theorem and an interpolation strategy to eliminate shear locking. Several numerical examples are discussed to demonstrate the accuracy of RZT(m) and related finite elements for static response, free-vibrations and critical load problems of sandwich structures.

Modular frame trusses of buildings

The paper describes space-planning and structural concept in source-efficient buildings that provides multiple functions of the rooms and large-span space.The main load-bearing structures of two adjacent storeys are metal trusses with parallel chords between which (between top and bottom chords) intermediate storeys are designed and the space between trusses is occupied by the free plan storeys. Bottom and top chords of the truss resist together with floor structure forming two-storey steel-reinforced concrete unit. To calculate value of deformation capacity for nodal connection a numerical experiment focused on modelling a part of building from solid finite elements has been performed. The results of performed analysis are the average values of stiffness of nodal interface of solid floor slab on corrugated deck and truss chords for finite elements KE 55 of typical layout (of flat finite elements). The obtained average values of stiffness were introduced into structural design of flat finite elements. Taking into account flexibility of floor slab that supported by middle trusses for the given structural concept leads to decreased span bending moments and increased support bending moments by 25% compared with hinge support of floor.

Реализация дискретно-связевой расчетной модели в плоскостных конечных элементах

Реализация дискретно-связевой расчетной модели в плоскостных конечных элементах

Development of a new finite element for plate and shell analysis by application of generalized approach to patch test

A triangular flat finite element with three nodes in the corners has been developed for analysis of Kirchhoff plates and shells within the framework of the extended interpretation of the Irons patch test. The condition of the bending displacements continuity in the case of non-constant strains is supposed to be violated not only on the boundaries but inside the area of an element as well. In general the typical approximations of the finite element method are implemented here in the limit of the infinitesimal elements. Thus it is possible to obtain the relatively simple but quite effective finite elements. The numerical results based on the classical tests demonstrate the high accuracy and quick convergence of the solutions obtained with the help of the presented finite element.

Fluid–structure interaction modelling of nonlinear aeroelastic structures using the finite element corotational theory

Abstract The application of the finite element corotational theory to model geometric nonlinear structures within a fluid–structure interaction procedure is proposed. A dynamic corotational approximately-energy-conserving algorithm is used to solve the nonlinear structural response and it is shown that this algorithm's application with a four-node flat finite element is more stable than the nonlinear implicit Newmark method. This structural dynamic algorithm is coupled with the unsteady vortex-ring method using a staggered technique. These procedures were used to obtain aeroelastic results of a nonlinear plate-type wing subjected to low speed airflow. It is shown that stable and accurate numerical solutions are obtained using the proposed fluid–structure interaction algorithm. Furthermore, it is illustrated that geometric nonlinearities lead to limit cycle oscillations.

An automatic hexahedral mesh generation for high-quality mesh by deformation and tree structure

An automatic mesh generator for hexahedral elements has already been proposed. However, the application of this generator to a model with both the hexahedral and the cylindrical objects results with generated meshes with large number of flat finite elements. It is known that a large number of flat elements lead to much lengthy finite element analysis (FEA) and lower accuracy of the obtained results. Therefore, the development of the versatile and high-quality automatic hexahedral mesh generator for models consisting hexahedral and cylindrical objects in the same model is strongly desired. In the proposed generation method, where the geometrical change of the model is employed, the generated mesh is composed mainly of well-shaped hexahedral elements. Moreover, the same number of boundary nodes for imposing periodical boundary conditions can be generated.

A simple finite element model for the geometrically nonlinear analysis of thin shells

A triangular flat finite element for the analysis of thin shells which undergo large displacements is proposed. It is based upon the geometrically nonlinear theory of von Karman for thin plates and the total Lagrangian approach. It has a total of only twelve degrees of freedom, namely, three translations at each vertex and one rotation at each mid-side. The stiffness matrix and the tangent stiffness matrix are derived explicitly. The element is tested against nonlinear patch test solutions and its performance is evaluated by solving several standard problems. The directional derivatives of the potential energy function required for the stability analysis are also provided.

3D eddy current analysis by the finite element method using double nodes technique

There are several difficulties in calculating eddy currents in plates with thin slits by the finite element method (FEM). Under the influence of flat finite elements at slits, the accuracy of analysis decreases and the computation time increases. Using the A-/spl phi/ method, we propose a novel technique, which overcomes those defects. The feature of the method is to adopt double nodes for the electric scalar potential /spl phi/ at slits, but not to the magnetic vector potential A. Adopting this technique, slits are equivalent to current barriers that have infinitesimal width. Some numerical results, which show the validity of the proposed method, are also presented. We analyze the magnetic fields of a double-sided linear induction motor with slits in a secondary plate, as a suitable model for proving the validity of the proposed method.

Rebuttal to Reply by Author to "Comment on 'Flutter of Flat Finite Element Panels in a Supersonic Potential Flow' "

Rebuttal to Reply by Author to "Comment on 'Flutter of Flat Finite Element Panels in a Supersonic Potential Flow' "

Nonlinear analysis of free-form shells by flat finite elements

The paper describes a general formulation for geometrically nonlinear analysis of shells using very simple flat finite elements. The approach is based on the “updated Langrangian” description of motion (co-rotational coordinates), in which the geometry of the shell structure is continuously updated during deformation to establish new reference configurations. The numerical solution technique adopted in the paper allows tracing of the entire nonlinear load-deflection path including unstable branches in the solution space. Numerical studies are presented in order to demonstrate the accuracy and efficiency of the proposed method.

Comment on "Flutter of Flat Finite Element Panels in a Supersonic Potential Flow"

about Mach 3, cone angle and bluntness ratio are equally important; and above Mach 3, bluntness is the relatively stronger parameter in establishing the base pressure level. The validity of the correlation is demonstrated by comparison with specific 9 and 10 deg cone data for sharp and 0.3 bluntness ratio noses which are given in Fig. 4. Data for other cone angles and bluntness ratios exhibit an equally good agreement with the prediction as would be expected based on Fig. 2; however, all of these data are not given in Fig. 4 for clarity. Also, total drag measurements obtained in an aeroballistics range on sharp 10-deg semiangle cones during the course of the transition experiments reported in Ref. 4 were analyzed. A sting free, flight base pressure was extracted from these data by subtracting a calculated forebody drag (pressure and skin friction) from the measured total drag. This calculations can be made with great precision for the sharp slender cone in question since the location of transition was measured. The relatively precise free-flight base pressure results obtained in this manner are given in Fig. 4 and further confirm both the absence of sting effects and the validity of the correlation. Even at Mach numbers in excess of eight, base pressure predictions utilizing this technique are in good qualitative agreement with the available turbulent data for sharp or small bluntness cones (up to Mach ~ 20). Summary At supersonic speeds, the base drag of sharp or blunt conical bodies represents a significant fraction of the total

Flutter of Flat Finite Element Panels in a Supersonic Potential Flow

A finite element formulation and a solution procedure are developed for the flutter analysis of twodimensional flat panels with one surface exposed to a supersonic potential flow and supported at the leading and trailing edges. The aerodynamic forces due to supersonic flow are obtained from the exact theory for linearized two-dimensional unsteady flow where no limitations on the order of the frequency are imposed. Thus the Mach number need not be limited to beyond approximately 1.6. When using this theory, the aerodynamic matrix becomes location-dependent and must be formulated for each element. This difficulty is overcome by first assembling the element shape functions for the entire structure and then finding the aerodynamic forces and the element aerodynamic matrix by numerical integration. The effects of structural damping and initial inplane tension are included. Examples for finding the panel thickness required to prevent flutter at various Mach numbers are demonstrated and the results are compared with an alternative Galerkin's modal solution as well as experiments.