Solid Element Model Research Articles

Punching of RC slabs without transverse reinforcement supported on elongated columns

The paper investigates the influence of support elongation on punching resistance at internal slab column connections without shear reinforcement. Nonlinear finite element analysis (NLFEA) with 3-D solid elements is used to study the influence of column elongation on stress and strain in the slab around the column. Punching failure is shown to be triggered by localised peaks in shear stress around the corners of the support. Significantly, one-way shear is shown to increase the shear resistance of slabs supported on columns with cross sectional dimensions greater than around six times the slab effective depth (d). The common laboratory practice of supporting slabs in punching tests on elongated plates rather than columns is investigated numerically and is found to be reasonable despite uplift occurring in the central region of elongated plates. NLFEA with solid elements gives useful insights into punching failure but nonlinear shell elements are better suited to the practical assessment of slabs in building structures. The disadvantage of conventional nonlinear shell elements is that shear failure can only be detected through post processing of results. To circumvent this, the authors have previously developed a novel modelling approach in which 3-D joint elements are used to connect shell elements located to either side of a punching control perimeter positioned at 0.5d from the column face. The joint shear resistance is calculated using the Critical Shear Crack Theory (CSCT) in which punching resistance is related to slab rotation. Based on insights gained using the solid element modelling, this paper extends the use of the joint model to the modelling of punching failure at elongated supports by including one-way joints to model linear shear.

Numerical investigation of stress concentration factor induced by multiple scenarios of adjacent corrosion pits

This paper simulates the stress concentration caused by adjacent corrosion pits using experimental and numerical method. A detailed three-dimensional finite element solid model is established and validated by individual notched specimen. The shape factor and shape transformation factor are proposed to represent the relationship between the stress concentration factor induced by individual ellipse and triangular notch. A distance factor and an angle factor are integrated to represent the stress concentration factor resulted from adjacent notches. Quantitative expressions for stress concentration factors in multiple scenarios are obtained. The results show that the adjacent notches distributed along the longitudinal direction of rebar with a relative angle of 0° induced stress concentration factor is close to that the individual ellipse notch when the notch spacing exceeds a critical distance (6 mm), and using the latter scenario instead of the former scenario for simplified modelling process has an insignificant effect on stress concentration. For the adjacent notches distributed along the cross-section direction of rebar with a relative angle of 90°, the maximum stress is approximately 40% higher than that of an individual notch in the analyzed range of depth. Several suggestions are also provided based on the present study.

Finite Element Calculation and Analysis of Stress and Deformation Characteristics of Arch Dam

The arch dam is a high-order and ultra-static overall space shell structure on the consolidation and bedrock, and its geometry, boundary conditions and stress state are complex. The three-dimensional finite element solid model of arch dam is established, and the stress and deformation characteristics of the actual dam project are calculated. It is concluded that there is a large tensile stress at the dam at the arch crown section and a large compressive stress at the dam site. The transverse displacement of the body occurs at the abutment of the upstream and downstream faces. The calculation results are in accordance with the stress and deformation characteristics of the arch dam, and the maximum stress and maximum displacement meet the design requirements of the arch dam.

Seismic assessment of deep water bridges in reservoir considering hydrodynamic effects using endurance time analysis

Hydrodynamic effects have a significant impact on the seismic performance of deep water bridges in reservoir. Currently, three-dimensional numerical fluid-structure interaction models are widely used for seismic analysis of such bridges with huge computational time. In this paper, endurance time analysis (ETA) was used as an alternative approach to reduce the simulation effect. The effectiveness and accuracy of this approach were studied by comparing with incremental dynamic analysis (IDA). Firstly, an iterative method based on spectral modification techniques of ground motions was proposed in order to reduce the computational time in developing the endurance time acceleration functions (ETAFs). Then, the generated ETAFs compatible with Chinese seismic code were validated with IDA curves using a coupled water-pier numerical system based on potential-based fluid elements. Finally, a typical deep water bridge in a reservoir was selected as a case study and was modeled by a three-dimensional solid element model to investigate the seismic responses of bridges at different water depths. The accuracy of added-mass method with fiber-based beam-column element models was also evaluated. It can be concluded that the proposed method for generating the ETAFs is an efficient alternative method and the endurance time method can provide sufficiently accurate estimation of hydrodynamic effects.

Beam-column modeling and seismic fragility analysis of a prestressed segmental concrete tower for wind turbines

As the development of wind energy in earthquake areas advances, the seismic performance of concrete supporting towers has become an important subject. A beam-column model is developed for a prestressed segmental concrete tower supporting a wind turbine considering the properties of dry joints. The proposed model is in good agreement with the solid element model deformation results and the field test modal results. Based on the beam-column model, nonlinear time history analyses considering uncertainties are conducted to evaluate the behavior of the prototype tower under earthquake action. In the process, a new engineering demand parameter, called the average curvature, is defined. The results are compared with those based on a conventional engineering demand parameter. The availability of the prototype tower under earthquake action and the effectiveness of the newly defined engineering demand parameter are validated.

Three-dimensional finite element modeling of rotary-draw bending of copper-titanium composite tube

The copper-titanium bimetallic composite bent tube, which could integrate the advantages of physical, chemical, and mechanical properties of two materials, shows an urgent application demand prospect in mechanical manufacturing, marine operations, and other industrial fields. This paper develops a research on the modeling of rotary-draw bending of copper-titanium composite tube by using two kinds of grid elements S4R and C3D8R, respectively. The contact problem of base tube and covered tube is set as coulomb friction contact mode, whose optimal friction coefficient is obtained by pressure-shearing experiment and its simulation. The springback model is established by considering the contact action of the two tubes. Finally, the S4R shell FE model is compared with the C3D8R solid FE model from the two aspects of section deformation and springback. It is found that the shell element model is accurate in predicting the springback and section deformation, while the solid element model has a large deviation from the experimental results in predicting the section deformation. In order to gain a deeper understanding of the plastic deformation behavior of the bimetallic composite tube, the tangential stress, equivalent stress, equivalent strain, and damage values have been studied. Results show that (1) there is no significant uneven deformation between the base tube and the covered tube, which will not produce obvious wrinkling and section distortion even without the filling of the mandrel dies. (2) Sliding and stratification are existing between the base tube and the covered tube in the bending process. (3) The force of the dies on the base tube is transmitted through the side surface contact between the base tube and the covered tube. (4) The maximum damage value of the covered tube is larger than that of the base tube. This research will promote the development of precise plastic processing technology and play a role in the research of secondary plastic forming of metal composite tubes.

Comparison of FEA for Different Type Element Models of Open Thin-Walled Member

Open thin-walled beam is widely used in civil engineering. The open-walled section model is significantly different from closed section model because the torsional stiffness is small. In order to select an appropriate analytical model for the open-walled section member, three different type element models (beam element model, shell element model and solid element model) for open-walled section members are adopted in ABAQUS/Standard and the low-frequency cyclic loading is used in the analysis process in this paper. The hysteretic curves and skeleton curves of the different element model are obtained using above method, and the bearing capacity, stiffness and the computation time are compared. The analysis results show that the results of three type element models are in good agreement, and the computational efficiency of the three type element models varies significant differences. Hence, it can be concluded that the accuracy of computation results can be guaranteed using those three type element models, and the beam element model has the highest computational efficiency.

Construction and analysis of finite element model of defected articular cartilage.

In order to construct a finite element model of defected articular cartilage, the mechanical behavior and degeneration of articular cartilage after injury were studied. The simplified analytical models of normal and defected articular cartilage and finite element models were established, respectively. Firstly, the analytical solution model and finite element model of hollow defect were constructed by using the elasticity theory of multi-hollow medium. Then, the analytical results of each model were calculated and programmed. The software MATLAB was used for programming calculation. Finally, a finite element solid model of defected articular cartilage was established by using human femoral joint. The solid model was analyzed and calculated by magnetic resonance imaging (MRI). The results showed that when the radius of articular cartilage defect r = 0, i.e. there was no defect in articular cartilage, the internal pore pressure of the defect cartilage was the largest, and its pore pressure value was pa. When the depth of articular cartilage defect r = 0, i.e. there was no defect in articular cartilage, the internal pore pressure of the defect cartilage was the largest, and its pore pressure value was pa, and it gradually decreased towards the outer boundary of cartilage. When the surface of femoral cartilage began to defect, with the increase of the depth of the defect (from shallow to deep), the maximum pore pressure in the defect cartilage gradually decreased, but the speed is slowly. With the increase of the defect radius, that is, the area of the defect, the maximum pore pressure in the defect cartilage gradually decreased. When there was no defect of articular cartilage, the internal pore pressure of the defect cartilage was the maximum, the value of pore pressure was pa, the value of pore pressure at the contact position of femoral cartilage was the largest, and it gradually decreased towards the outer boundary of cartilage. At the same location, the pore pressure of normal cartilage was significantly higher than that of defected cartilage. With the change of defect location, the pore pressure was reduced accordingly. Moreover, when the defect position moved from the outside to the inside, the corresponding pore pressure value was decreased gradually. To sum up, the finite element model of defected articular cartilage based on porous elasticity theory has better calculation ability, which proves the validity of the finite element software, and provides a strong basis for future model establishment and clinical treatment of articular cartilage.

Improved Woodbury approximation approach for inelasticity-separated solid model analysis

Solid elements are widely implemented in conventional finite element method (FEM), but they also consume more computing resources relative to the bar, beam and shell elements because of the high dimensional tangent stiffness matrix recalculation and factorization. In this work, an inelasticity-separated solid element model and an efficient numerical solution procedure are proposed for the material nonlinear analysis of three-dimensional (3D) entity structures. This solid element model was developed within the framework of the inelasticity-separated finite element method (IS-FEM) presented in prior studies [1], the computational efficiency of IS-FEM is better than that of conventional FEM for the local material nonlinearity problem when using the Woodbury formula. The tangent stiffness matrix of a structure is expressed by the sum of the invariant global stiffness and another changing Schur complement modification with a low-rank. However, a nonlinearity problem with solid elements may have more inelastic degrees of freedom (IDOFs), thus, the efficiency of IS-FEM is low due to the high-rank Schur complement modification. This study improved the solution procedure of the Woodbury approximation Method (WAM), which applies the combined approximation (CA) approach within the framework of the Woodbury formula. The new derived solution scheme only contains limited back-substitutions of the global initial stiffness matrix and product of the sparse matrix and vector during a certain iteration step, which completely avoids the Schur complement matrix factorization and the constant matrix precalculation and storage process. Time complexity analysis indicates that the efficiency of the improved methodology is greatly enhanced relative to both the conventional FEM and the IS-FEM with the exact Woodbury formula, and the ratio of the efficiency improvement increases with an increase in the degrees of freedom (DOFs). Finally, the numerical examples demonstrate the validity and efficiency of the presented solid element model and the improved solution procedure.

Modelling the test methods used to determine material compatibility for hydrogen pressure vessel service

This work aims to create finite element models to simulate the three ISO 11114-4 test methods applicable to hydrogen gas cylinders, coupled with calibrated constitutive models, to predict the deformation response of each. Experimental measurements are used to calibrate a monotonic constitutive model and a constitutive model of cyclic deformation. Six finite element solid models are discussed: monotonic tensile test of dog bone-shaped specimens, strain-controlled fatigue test of dog bone-shaped specimens, ISO test Method A, ISO test Method B, and ISO Method C (from ISO 11114-4), and a gas cylinder. Each finite element solid model is paired with the appropriate constitutive model based upon loading conditions. The modeling results are then combined with a new damage parameter in an attempt to compare each of the test methods to the others, as well as to in-service conditions. It is shown that the proposed damage parameter may be used to correlate all test methods considered (except for ISO Method A, a burst-disc test) as well as in-service conditions. The calibrated damage parameter may be coupled with any geometry, loading condition, and boundary condition modeled within a finite element package to predict the onset of critical damage in the material for which the coupled constitutive model is calibrated to. Parametric modelling study results provide estimated cycles to the onset of crack extension for DOT 3AA cylinders having varying sizes of internal thumbnail-shaped cracks. This work provides the baseline for measurements and models in air, with similar work in hydrogen to follow.

Performance evaluation of RC frame with RC wall piers equipped with unbonded steel rod dampers subjected to in-plane loading

Brittle shear failure of partial Reinforced Concrete (RC) wall pier system is usually observed in post-earthquake investigations, which affects the building functions seriously. A new RC wall pier system with unbonded steel rod dampers is introduced in this study. Numerical simulation using solid element method, validated by existing experimental results, was adopted firstly to investigate the behaviors of dampers, lateral force capacity, stiffness degradation, and ductility of the frame with the new RC wall pier system considering the influence of the dampers and the frame axial compression ratios. To decrease the huge computational costs of the solid element model, macro element model was further developed and verified. Performance evaluation of a twelve-story RC frame structure with three models of RC wall piers, namely damper model, slit model and rigid model, was conducted with the macro element model. Results show that RC frame with RC wall piers equipped with dampers possesses a stable lateral, and the designed dampers provide more than 20% of the lateral force to the frame. It is advised that the axial compression ratio of frame column shall be within 0.1 from the perspectives of plastic regions of dampers and lateral force capacity of frame. The nonlinear responses of the new RC wall pier system can be well captured by the macro element model with less computational costs. By comprehensively considering the structural drift ratios, the energy dissipation and the shear force in the frame beam, the damper model is suggested to be the best among the three models. The new RC wall pier system highlights an alternative for the conventional RC wall pier systems in the engineering practice.

Finite element analysis on the seismic behavior of side joint of Prefabricated Cage System in prefabricated concrete frame

The Prefabricated Cage System (PCS) has the advantages of high bearing capacity and good ductility. Meanwhile, it is convenient for factory production and it is beneficial to the cost savings, construction period shortening. Side joint is the weak region of PCS concrete frame and has great influence on seismic behavior of the whole structure. Thus systematically study on the seismic behavior of PCS concrete side joint is necessary. This paper presents a finite element study on behavior of the side joint under seismic loading. In the finite element model, PCS concrete and the reinforced concrete (RC) is modeled by the solid element and fiber-beam element, respectively. The numerical results is compared with the experimental results and it is found that the results of model based on fiber-beam element is in better agreement with the experimental results than solid element model. In addition, the overall seismic behavior of the side joints in PCS concrete is better than that of the RC with the same strength.

Mechanical Property Study on the Planting Bar Strengthening Structure based on Midas/civil Solid Element

When using Midas/civil solid element modeling to analyses a simple strengthening model by enlarging section method, it is found that the temperature stress of the model without implant reinforcing bars is very large under the overall temperature load, which is inconsistent with the actual engineering situation. When the model is implanted the reinforcing bars, the temperature stress generated by the overall temperature load becomes normal. It can be concluded that the defects of temperature stress anomalies caused by different linear expansion coefficients of different materials can be effectively corrected by implanting reinforcing bars in solid element models. When the defect of solid element model is corrected, its application prospects will become extremely broad, and it may eventually replace the calculation methods of internal force, stress and displacement provided by current engineering specifications.

Studying rigidity of the welded liner - composite shell construction

The mechanical behaviour of an aluminium welded liner in a cylindrical metal composite vessel of high pressure made by winding on a linear carbon-filled plastic tape with tension is investigated. The resulting pressure of the wound composite shell on the welded liner is simulated by cooling the shell. It is believed that the weld is obtained by friction welding and has characteristics that are reduced in relation to the base material of the liner. The problem is solved in a geometrically and physically nonlinear formulation using a 3D solid element model, taking into account technological deviations and in real (current) time. The calculations were performed in the LS-DYNA software package in a dynamic formulation. It is shown that liner delamination from the sheath starts from the side of the circumferential weld in the area of technological deviations.

Discrete solid element model applied to plasticity and dynamic crack propagation in continuous medium

In this work, the discrete solid element model (DSEM) applied to plasticity and dynamic crack propagation problems in the continuous medium is developed and implemented. First, the Drucker’s postulate and the consistency condition are used to establish the plastic flow rule in the DSEM. The plastic scale factor which characterizes the plastic displacement increment of spherical elements is derived by the classical plastic mechanics. The elastoplastic contact constitutive equations of the strain-hardening material are established, which can be used for elasticity, unloading and loading. Second, to accurately simulate the mechanical behavior of continuity, the spring stiffness of spherical elements on the boundary of the DSEM is strictly deduced using the principle of conservation of energy, and the relationship between the spring stiffness and the continuous constitutive parameters is established. Third, the bilinear contact softening model is adopted to simulate the crack propagation in the continuous medium. The criteria for the crack propagation based on the fracture energy of the material are developed. The numerical examples are presented to show the capability and effectiveness of the DSEM in simulating the dynamic buckling and crack propagation problems. The obtained results are in agreement with experimental and numerical results published by other researchers.

STABILITY AND SEISMIC VULNERABILITY OF THE STYLITE TOWER AT UMM AR-RASAS

The stability and vulnerability analyses carried out on the Stylite tower at Umm ar−Rasas, Jordan, are presented in this paper. The tower is a unique example of this kind of structure still existing. The soil and the structural material were analyzed by means of in situ ex− perimental tests. These consisted of Schmidt−hammer tests on stone blocks and passive seismic measurements. The stability of the tower was first analyzed, assuming an elastic – perfect plastic behavior in compression for masonry. Then the push−over seismic analysis was carried out, which was based on a single−mode approach and a finite solid element modelling with a Drucker−Prager yield criterion for masonry. The work is propaedeutic to the design of a retrofit intervention.

Analytical behaviors of concrete-filled circular stainless steel tubular (CFCSST) stub columns under axial loading

The objective of this paper is to investigate the behaviors of concrete-filled circular stainless steel tubular (CFCSST) stub columns under axial loading. A fine finite 3D solid element model was established, and the FE results revealed that the increased ultimate bearing capacity of CFCSST stub columns compared with their carbon steel counterparts was mainly due to that the confinement effect of CFCSST stub columns was stronger than that of carbon steel counterparts and the stress contribution of stainless steel was higher than that of carbon steel. The stress nephogram was simplified reasonably in accordance with the limit state of core concrete and a formula was proposed to estimate the ultimate bearing capacity of CFCSST stub columns using superposition method. Finally, the difference of the experimental and predicted results using the proposed formula and the existing codes were illustrated.

Confinement coefficient of concrete-filled square stainless steel tubular stub columns

The objective of this paper is to investigate the confinement coefficient of concrete-filled square stainless steel tubular (CFSSST) stub columns under axial loading. A fine finite 3D solid element model was established, which utilized a constitutive model of stainless steel considering the strain-hardening characteristics and a triaxial plastic-damage constitutive model of concrete with features of the parameter certainty under axial compression. The finite element analysis results revealed that the increased ultimate bearing capacity of CFSSST stub columns compared with their carbon steel counterparts was mainly due to that the composite action of CFSSST stub columns is stronger than that of carbon steel counterparts. A further parametric study was carried out based on the verified model, and it was found that the stress contribution of the stainless steel tube is higher than the carbon steel tube. The stress nephogram was simplified reasonably in accordance with the limit state of core concrete and a theoretical formula was proposed to estimate the ultimate bearing capacity of square CFSSST stub columns using superposition method. The predicted results showed satisfactory agreement with both the experimental and FE results. Finally, the comparisons of the experimental and predicted results using the proposed formula and the existing codes were illustrated.

Modelling of fluid-structure interaction for moderate reynolds number flows using an immersed-body method

An unsteady Reynolds-averaged Navier–Stokes (URANS) model coupled with an immersed-body method is used to model fluid-structure interaction (FSI) for moderate Reynolds number flows. Particular attention is paid to the application of suitable flow boundary conditions with the immersed-body method. This model couples a combined finite-discrete element solid model and a finite element fluid model with the standard k−ε model. A thin shell mesh surrounding the solid surface is first used as a delta function to apply the interface boundary conditions for both the URANS model and the momentum equation. In order to reduce the computational cost, a log-law wall function is used within this thin shell to resolve the flow near the solid wall. To improve the accuracy of the wall function, a novel shell mesh external-surface intersection approach is introduced to identify sharp solid-fluid interfaces. More importantly, an unstructured anisotropic mesh adaptivity is used to refine the mesh according to the interface and the velocity, which improves the accuracy of this immersed-body URANS model with use of a limited number of fluid cells. This immersed-body URANS method is validated by several test cases and results are in good agreement with both experimental and numerical data from the literature.

Static assessment of plain/notched polylactide (PLA) 3D‐printed with different infill levels: Equivalent homogenised material concept and Theory of Critical Distances

AbstractA novel approach based on the equivalent homogenised material concept and the theory of critical distances is formulated to perform static assessment of plain/notched objects of polylactide (PLA) when this polymer is additively manufactured with different infill levels. The key idea is that the internal net structure resulting from the 3D‐printing process can be modelled by keeping treating the material as linear elastic, continuum, homogenous, and isotropic, with the effect of the internal voids being taken into account in terms of change in mechanical/strength properties. This idea is initially used to assess the detrimental effect of the manufacturing voids on the static strength of the plain (ie, unnotched) material. This is done by addressing this problem in a Kitagawa‐Takahashi setting via the Theory of Critical Distances. Subsequently, this approach is extended to the static assessment of notched components of 3D‐printed PLA; ie, it is used to take into account simultaneously the effect of both manufacturing voids and macroscopic geometrical features. The accuracy and reliability of this design methodology were checked against a large number of experimental data generated by testing, under axial loading, plain specimens, as well as notched samples (including open notches) of PLA. These specimens were manufactured by making the infill level vary in the rage 10% to 90%. This validation exercise allowed us to demonstrate that the proposed approach is highly accurate, returning estimates falling within an error interval of ±20%. This remarkable level of accuracy strongly supports the idea that static assessment of 3D‐printed materials with complex geometries and manufactured with different infill levels can be performed by simply post‐processing conventional linear elastic finite element (FE) solid models, ie, without the need for modelling explicitly the detrimental effect of the manufacturing voids.