8-node Solid Element Research Articles

One-point quadrature ANS solid-shell element based on a displacement variational formulation Part I – Geometrically linear assessment

A demonstration of a computationally efficient, physically stabilised one point-quadrature solid-shell finite element in pure displacement variational formulation and within the context of hierarchical displacement modes is presented in this paper. The displacement field of the 24 degree of freedom 8-node solid finite element is enhanced by a hierarchical, thickness-wise, quadratic displacement field and associated single displacement degree of freedom. The displacement enhancements expand the covariant element strain space resolving thickness locking and in combination with the assumed natural strain approach, attenuates shear and trapezoidal locking in thin shell simulations. Formulated within the recent framework of the reduced integration element technology and hourglass physical stabilisation, a locking free, 8-node solid-shell element for general three dimensional shell analysis is obtained. The theoretical relevance and applicability of the proposed displacement-kinematics 8-node solid-shell element offering comparable accuracy and performance flexibility as physically stabilised reduced integration solid-shell elements based on mixed and EAS variational statements is demonstrated in selected linear numerical benchmark problems.

A Finite Element Analysis of Bearing Resistance of Timber Loaded through a Steel Plate

Decrease projected length of bolts due to bending deformation in timber joints compresses the steel washers onto timber member and increases lateral resistance of the joints. As this lateral strength increase primarily depend on bearing characteristics of timber beneath the steel washers, a finite element analysis was performed to predict their bearing-embedment behavior. A 3-D finite element model consisting of 8-node solid and contact pair elements was developed using ANSYS assuming an anisotropic plasticity model for timber and an elastic-perfectly plastic model for the washers. Material constants for both steel washer and timber member were obtained from previous test data. The results of the analysis were in good agreement with the experimental load-embedment curves as well as the analytical curves obtained in a previous study based on a rigid-body-spring-model. The same approach was also used to evaluate the effective bearing length (under uniform compression) of a 50 mm depth timber block partially compressed.

분포하중이 철근 콘크리트 슬래브의 동적 거동에 미치는 영향

This study has been carried out to investigate the dynamic characteristics of RC slabs. For this purpose, the 20-node solid element has been used to discretize the RC slabs into two parts of concrete and rebar. The material non-linearity considering elasto-visco plastic model and the smeared crack model have been adopted in the finite element formulation. The applied load can handle step load, load intensity of harmonic load, area of distributed load and frequency. The frequency of harmonic load has an significant effect on dynamic behaviour in terms of displacement. As the frequency is increased, the effect of load amplitude is more serious. Especially, if the frequency of harmonic load exceeds 30 Hz, it is noted that the displacement by harmonic load is greater than that by step load. In case of harmonic load, the damping effect shows no certain tendency with respect to frequency of load. In details, the damping is effective when the frequency of harmonic load is 2 Hz, but there is no consistent tendency according to damping ratio. The dynamic response when the frequency of harmonic load is 3 Hz shows same result for undamped case as well as for damped case with 5% damping ratio. It is also noted that we can get the largest deflection for damped case with 1% damping ratio. However, there is not any damping effect when the frequency of harmonic load is greater than 4 Hz.

Eight‐node shell element based on incompatible modes

AbstractThis paper concerns the shell element formulation used for linear analysis. Introduction of hierarchical incompatible modes into the ordinary 8‐node solid element is very effective to obtain the rational deflection–rotation relationship. An efficient revision scheme without using numerical volume integration is developed to ensure the satisfaction of the patch test. A lot of numerical tests are carried out for the validation of the present element. Numerical results show that the element can give satisfactory accuracy and convergence, especially for moderately thick shells. Copyright © 2008 John Wiley & Sons, Ltd.

A mesh distortion tolerant 8-node solid element based on the partition of unity method with inter-element compatibility and completeness properties

An 8-node solid element is developed based on the partition of unity method. The formulation uses isoparametric shape functions of the classical 8-node solid element to form the partition of unity and a modified least squares shape functions based on the point interpolation method for the local approximation. The motivation for the formulation is to obtain an element that ensures both inter-element compatibility and completeness properties. An element that simultaneously satisfies both these properties is capable of good performances under distorted mesh shapes. This is reflected in the numerical experiments reported in this paper.

A32 シャフトを有するゴルフ・クラブヘッド模擬体とボールとの衝突解析(ゴルフ,他)

The purpose of this study is to construct a finite-element (FE) model which can accurately simulate the behaviour of golf impacts, and to investigate the effect of a shaft on clubhead upon the rebound behaviour of a ball, by conducting an FE analysis of a ball colliding with a simplified club. The clubs were constructed by holding the simplified clubheads by the locking ring which is fitted onto a steel shaft. Three clubheads (circular hollow bodies) of constant mass, made of a titanium alloy, with increasing loft angle were manufactured based upon the mass, volume and position of centre of gravity (COG) of commercial clubheads. The FE models of the clubheads, which consisted of clubheads, locking ring and shaft, with linear elasticity, were constructed. The FE model of the ball consisted of 8-node solid elements, and the material model was expressed as a viscoelastic model with hyperelasticity. Impact experiments were also conducted to confirm the accuracy of the FE models, by comparing the results of the experiments to those of the FE analyses. The results of impact simulations closely matched the experimental results. The impact behaviour was analysed by varying the impact point of the ball colliding with the full clubs and the singular clubheads; the results for the collision between the ball/clubs and ball/clubheads were compared. The difference between the two extreme values for the rebound angle and the spin rate in the case of the club impacts tended to become smaller than that of the clubhead impacts. This tendency is estimated to depend on the relationship between the shaft position and the loft angle/COG of the clubhead.

Stress and strain concentration factors of completely overlapped tubular joints under lap brace IPB load

This paper presents parametric equations to predict the stress concentration factor (SCF) of completely overlapped tubular joints under lap brace in-plane bending (IPB) load. A completely overlapped tubular joint specimen is first tested for the verification and calibration of finite element (FE) models. The experimental results showed that the strain distribution near the weld toe is fairly linear. The maximum strain concentration factor (SNCF) of the joint occurs at the lap brace crown heel under IPB load. For the FE analysis, both 8-node thick shell and 20-node solid elements are suitable for modelling the joint. A set of parametric equations is proposed for predicting the SCF of completely overlapped tubular joints based on 5184 FE models. The parametric equations are verified against the acceptance criteria of Fatigue Guidance Review Panel. The assessment of the proposed equations is based on the database of FE analysis and test results. The comparison of SCF between the proposed parametric equations and the existing T / Y -joint parametric equations showed that the results do not agree reasonably well under IPB load.

Stress and strain concentrations of completely overlapped tubular joints under lap brace OPB load

The stress and strain concentrations of a completely overlapped tubular joint specimen are experimentally investigated under lap brace out-of-plane bending (OPB) load. The experimental results showed that the strain distribution near the weld toe is fairly linear. The maximum strain concentration factor of the joint occurs at the through brace saddle near the lap brace. For the finite element (FE) analysis, both 8-node thick shell and 20-node solid elements are suitable for modelling the joint specimen. A set of parametric equations is proposed for predicting the stress concentration factor (SCF) of completely overlapped tubular joints based on 5184 FE models. The parametric equations are verified against the acceptance criteria of Fatigue Guidance Review Panel. The assessment of the proposed equations is based on the database of FE analysis and test results. The comparison of SCF showed that the existing T/Y-joint parametric equations for predicting the SCF of completely overlapped tubular joints are inappropriate under OPB load.

Determining the effective width of composite beams with precast hollowcore slabs

This paper evaluates the effective width of composite steel beams with precast hollowcore slabs numerically using the finite element method. A parametric study, carried out on 27 beams with different steel cross sections, hollowcore unit depths and spans, is presented. The effective width of the slab is predicted for both the elastic and plastic ranges. 8-node three-dimensional solid elements are used to model the composite beam components. The material non-linearity of all the components is taken into consideration. The non-linear load-slip characteristics of the headed shear stud connectors are included in the analysis. The moment-deflection behaviour of the composite beams, the ultimate moment capacity and the modes of failure are also presented. Finally, the ultimate moment capacity of the beams evaluated using the present FE analysis was compared with the results calculated using the rigid - plastic method.

두꺼운 링의 고유진동 해석

In this paper, we have systematically formulated the equations concerned to the in-plane and out-of-plane motions and deformations of a thick circular beam by using the kinetic and strain energies in order to analyse natural frequencies of a thick ring. The effects of variation of radius of curvature across the cross-section and also the effects of bending shear, extension and twist are considered. The equations of motion for natural vibration analysis of a ring are obtained utilizing the cyclic symmetry of vibration modes of the ring. The frequencies calculated using thick ring model and thin ring model are compared and discussed with the ones obtained from finite element analysis using the method of cyclic symmetry with 20-node hexahedral solid elements for rings with the different ratio of radial thickness to mean radius.

A resultant 8-node solid-shell element for geometrically nonlinear analysis

A new resultant force formulation of 8-node solid element is presented for the linear and nonlinear analysis of thin-walled structures. The global, local and natural coordinate systems were used to accurately model the shell geometry. The assumed natural strain methods with plane stress concept were implemented to remove the various locking problems appearing in thin plates and shells. The correct warping behavior in the very thin twisted beam test was obtained by using an improved Jacobian transformation matrix. The 2 × 2 Gauss integration scheme was used for the calculation of the element stiffness matrix. From the computational viewpoint, the present solid element is very efficient for a large scale of nonlinear modeling. A lot of numerical tests were carried out for the validation of the present 8-node solid-shell element and the results are in good agreement with references.

Three-dimensional stresses in adhesively bonded lap joints with non-identical adherends

This paper is concerned with the three-dimensional stress distributions in adhesively bonded joints with non-identical adherends and different geometrical dimensions and materials. The constitutive relations for the adhesive are developed using a modified pressure-dependent von Mises yield function and elasto-plastic idealization for the experimental stress-strain curve. The adherends and adhesive layers are both modelled using 20-noded solid elements. Observations have been made in particular on peel and shear stresses in the adhesive layer. Finite element results are found to match reasonably well with analytical solutions. Peel, shear and bending stresses in the lap joint address the three-dimensional behaviour prevailing in the single lap joint structure.

Parametric equations for stress concentration factors in completely overlapped tubular K(N)-joints

This paper presents parametric equations to predict the stress concentration factors (SCF) of completely overlapped tubular K(N)-joints under lap brace axial compression. 192 finite element (FE) models of the joint have been created for the parametric study using a commercial FE package, MARC. In the analysis, both 8-node thick shell and 20-node solid elements are found suitable for modelling the joint. The comparison of strain concentration factors (SNCF) between the FE models and the tested specimen shows that the difference is less than 0.42. However, in view of the computational effort, the FE model with 8-node thick shell element is used for the parametric analysis. The study reveals that the effect of through brace to chord wall thickness ratio on SCF of the joint is most crucial. The maximum SCF occurs on the through brace saddle near the lap brace. The gap size on the through brace surface between the outer surfaces of the chord and the lap brace significantly affects the SCF. Based on the FE data, a set of parametric equations is derived to predict the SCF of the joint. The reliability of the equations has been verified against the requirement of the Fatigue Guidance Review Panel.

Finite Element Analysis of Steel-Concrete Composite Girders

Finite element models for the analysis of solid slabs and precast hollow core slabs composite girders are presented. For both models, 8-node three-dimensional solid elements are used in the analysis. The material non-linearity of all components of the composite girders is taken into consideration. The non-linear load-slip characteristics of the headed shear stud connectors are included in the models. The models predict load – deflection behaviour and stress distribution along the length of the beam. Good agreement is obtained between the models and results previously published.

Deformation Analysis of 3D Braided Structural Composites

A nonlinear finite element technique is used to simulate and analyze the deformation behavior of 3D braided composites. The finite element displacement formula is derived from the geometric nonlinear behavior of braided composites. The integral relevant to the element stiffness matrix is simplified by selecting a 20-node hexahedral solid element. The Gauss-Legendre quadrature is used to compute the element matrix. A program referred to as SNLFEDA (Simulation of Nonlinear Finite Element Deformation Analysis) is developed. Tension, compression, and bending of 3D braided composites is simulated, and the results' of these simulations are supported by the experimental data and the values predicted by previously published elastic modulus models.

Three-dimensional Material and Geometrical Nonlinear Analysis of Adhesively Bonded Single Lap Joint

The paper presents 3-D viscoplastic analysis of adhesively bonded single lap joint considering material and geometric nonlinearity. Total Lagrangian formulation is used to develop a 3-D finite element for geometri.c nonlinear analysis. The overall geometry of the single lap joint, the loading, and the boundary conditions has been considered, both according to the ASTM testing standards and from those adopted in earlier investigations. The constitutive relations for the adhesive are developed using a pressure-dependant (modified) von Mises yield function and Ramberg-Osgood idealisation for the experimental stress-strain curve. The adherends and adhesive layers are both modelled using 20-noded solid elements. However, observations have been made, in particular, on peel and shear stresses in the adhesive layer, which provide useful insight into the 3-D nature of the problem.

Upgrading ductility of RC beam-column connection with high performance FRP laminates

Strengthening and retrofitting of the reinforced concrete beams, which have been designed and built in the past, is one of the most important issues in structural engineering. In this study, reversal loading represents seismic excitation. The criterion for upgrading a RC joint against such loading is increasing its strength and ductility. Using composite fabrics does such enhancement. In this direction, FEM is adopted to analyze the problem, The non-linearity of concrete material, such as tension cracks and compression crush, are included. The steel bars behavior is considered as bilinear elasto-plastic, and Tsai-Wu criterion is used to control FRP failure. 8-Node solid element, 3-D link element, and layer shell element are used for modeling of concrete, steel rebar and FRP laminate, respectively, Both of the as-is and the retrofitted comer joints are subjected to quasi-static cyclic loading, and their performance is investigated and compared with each other, in terms of peak lateral load capacity, ductility, moment-rotation diagram, crack patterns and cracks width. The stacking sequence of FRP laminates is (45,45),, and it is made fi-om Glass/Epoxy materials. The results are presented in terms of load-deflection curves and hysteretic energy loops. The load-deflection curves, for both as-is and strengthened bearncolumn connections, are studied in details, and the influence of using the composite fabrics on continuity of joints, smearing the cracks and limiting their sizes, are considered. The behavior of retrofitted joints is significantly improved in terms of moment bearing capacity, ductility, axial load, and drift.

Topology and performance redesign of complex structures by large admissible perturbations

A methodology for topology redesign of com- plex structures by LargE Admissible Perturbations (LEAP) is developed. LEAP theory is extended to solve topology redesign problems using 8-node solid elements. The corresponding solution algorithm is developed as well. The redesign problem is defined as a two-state problem. State S1 has undesirable characteristics and/or performance not satisfying certain designer specifica- tions. The unknown State S2 has the desired structural response and locally optimum topology. First, the gen- eral nonlinear perturbation equations relating specific response of States S1 and S2 are derived. Next, a LEAP algorithm is developed which solves successfully two-state problems for large structural changes (on the order of 100%-300%) of State S2, without repetitive finite elem- ent analyses, based on the initial State S1 and the spe- cifications for State S2. The solution algorithm is based on an incremental predictor-corrector method. The op- timization problems formulated in both the predictor and corrector phases are solved using commercial non- linear optimization solvers. Minimum change is used as the optimality criterion. The designer specifications are imposed as constraints on modal dynamic and/or static displacement. The static displacement general perturba- tion equation is improved by static mode compensation thus reducing errors significantly. The moduli of elastic- ity of solid elements are used as redesign variables. The LEAP and optimization solvers are implemented in code RESTRUCT (REdesign of STRUCTures) which postpro- cesses finite element analyses results of MSC-NASTRAN. Several topology redesign problems are solved success- fully by code RESTRUCT to illustrate the methodology and study its accuracy. Performance changes on the order of 3300% with high accuracy are achieved with only 3-5 intermediate finite element analyses (iterations) to arrest

Finite dynamic element formulation for three-dimensional structures

Based on energy functional and with the inclusion of high-order incompatible dynamic displacement modes, a formulation for 3-D finite dynamic element method (DEM) is developed and a new 8-node solid element is derived in this paper. Numerical results exhibit that the present method provides the most economical and efficient solution when compared with the usual FEM and DEM. Copyright © 2000 John Wiley & Sons, Ltd.

21-node hexahedral isoparametric element for analysis of contact problems

Because the 20-node solid element of the serendipity family does not fulfil the physical contact requirements properly (the equivalent nodal forces include negative values) a 21-node three-dimensional transient element for the non-linear contact/friction problem is investigated. Construction of the shape functions is described. The proposed transition element is established by adding one node to the top or bottom face of the basic 20-node solid serendipity element for an effective connection between the contact region (21-node elements) and the rest of the structure (20-node elements) with minimum degrees of freedom possible. Comparisons with results calculated for the 3D-contact problem using the combinations of the 8-node element connected to 20-node finite elements prove the high accuracy and overall superiority of the present method. The numerical examples are shown to illustrate the validity and efficiency of the developed technique. The approach may be employed easily in existing computer codes. © 1998 John Wiley & Sons, Ltd.