Present Finite Element Results Research Articles

Finite element evaluation of bearing capacity factors for cutting face of open caissons

ABSTRACT Open caissons are massive foundations sunk to the required depth by excavating the soil in contact with the cutting edge of the caisson through the annular space of the shaft. The sinking of caisson initiates when the soil in contact with the cutting edge fails in bearing. The evaluation of bearing capacity of the cutting edge helps in proper planning of the excavation strategy, analysis and design of caissons. In the present study, the bearing capacity factors for the cutting face of open caisson are evaluated using finite element method for different configurations of the cutting edge, properties of the soil and depth of sinking. The cutting edge with varying radii ratio (ri /ro = 0.35 to 0.95) and different cutting angles (β = 30° and 45°) is considered. The Mohr–Coulomb model with non-associated flow rule is used in the two-dimensional finite element (FE) analysis. The bearing capacity factors for the cutting face of the open caisson are evaluated for different friction angles of the soil (ϕ = 5° to 35°). The depth of sinking is accounted for in the FE analysis by considering the soil present above the base of the cutting edge as surcharge. The present FE results are compared with the results available in the literature and presented in the form of ready-to-use charts and tables for design purposes.

Stress Intensity Factor and Elastic Crack Opening Displacement Solutions of Complex Cracks in Pipe Using Elastic Finite-Element Analyses

In the present paper, the closed-form expressions for the stress intensity factors (SIFs) and the elastic crack opening displacements (CODs) of complex-cracked pipes are derived based on the systematic three-dimensional (3D) elastic finite-element (FE) analyses. The loading conditions that are evaluated include global bending moment, axial tension, and internal pressure. In terms of geometries, the geometric variables affecting the SIFs and the elastic CODs of complex-cracked pipes, i.e., the crack angle of through-wall cracks (TWCs), the crack depth of fully circumferential, internal surface cracks in the inner surface of pipe, and the ratio of pipe mean radius to thickness, are systematically considered in the present FE analyses. The FE analysis procedure employed in the present study has been validated against the existing solutions for the circumferential TWC pipes. Using the present FE results, the shape factors of SIF and elastic COD for complex-cracked pipes are tabulated as a function of geometric variables. The results are applied for closed-form expressions of SIF and elastic COD when the pipe is subjected to simple loading conditions of bending, axial tension, or internal pressure. The proposed closed-form expressions can estimate SIF and elastic COD of complex-cracked pipes within maximum differences of 2.4% and 5.9% with FE results, respectively.

A novel size-dependent microbeam element based on Mindlin’s strain gradient theory

Based on Mindlin's strain gradient elasticity and Euler---Bernoulli beam theory, a non-classical beam element capable of considering micro-structure effects is developed. To accomplish this aim, the higher-order tensors of energy pairs in the energy functional are vectorized and written in the quadratic representation, from which the stiffness and mass matrices of the element are obtained. In comparison with the classical Euler---Bernoulli beam element, the new element needs one additional nodal degree of freedom (DOF) which results in a total of three DOFs per node. The formulation of the paper is general so that it can be reduced to that based on the modified couple stress theory, the modified strain gradient theory, and the classical elasticity theory. To show the reliability of the proposed element, the bending and free vibration problems of microbeams under different kinds of end conditions are addressed. It is revealed that the present finite element results are in excellent agreement with the ones achieved through analytical solutions.

Temperature-dependent buckling analysis of sandwich truncated conical shells with FG facesheets

In this study, an improved high-order theory is presented for temperature-dependent buckling analysis of sandwich conical shell with thin functionally graded (FG) facesheets and homogenous soft core. First shear deformation theory (FSDT) is used for the facesheets and cubic functions are assumed for the transverse and in-plane displacements of the core. The nonlinear Von-Karman type relations are used to obtain the strain components. The equilibrium equations are derived via principle of minimum potential energy. Analytical solution for static analysis of simply supported sandwich conical shells under axial in-plane compressive load and in the temperature environments is performed using Galerkin’s solution. Numerical modeling is made by ABAQUS finite element (FE) code. The comparison shows that the present results are in good agreement with the results in the literature and the present FE results.

Finite element simulation of wireless structural vibration control with photostrictive actuators

A recently emerging family of smart materials, photostrictive materials, exhibit large photostriction under uniform illumination of high-energy light. This photostriction mechanism arises from a superposition phenomenon of photovoltaic and converse piezoelectric effects. A photostrictive type of opto-electromechanical actuator activated by high-energy lights can introduce actuation and control effects without hard-wired connections. The control light intensity applied to the actuator is proportional to the transverse velocity at a positioned point, which is measured by a laser vibrometer. In this paper, photostrictive films are numerically analyzed to evaluate their use as wireless actuators for future remote vibration control of flexible structures. A novel opto-electromechanical solid shell finite element formulation is developed for accurate analysis of the multiple physics effects of photovoltaic, pyroelectric and thermal expansion of photostrictive materials. Available experimental data and analytical solutions have been used to verify the present finite element results. The simulation in this study demonstrates that the present formulation is very reliable, accurate and also computationally efficient and that the use of photostrictive actuators can provide good controllability of structural vibration.

COLLAPSE PRESSURE ESTIMATES AND THE APPLICATION OF A PARTIAL SAFETY FACTOR TO CYLINDERS SUBJECTED TO EXTERNAL PRESSURE

The present paper investigates the collapse pressure of cylinders with intermediate thickness subjected to external pressure based on detailed elastic-plastic finite element (FE) analyses. The effect of the initial ovality of the tube on the collapse pressure was explicitly considered in the FE analyses. Based on the present FE results, the analytical yield locus, considering the interaction between the plastic collapse and local instability due to initial ovality, was also proposed. The collapse pressure values based on the proposed yield locus agree well with the present FE results; thus, the validity of the proposed yield locus for the thickness range of interest was verified. Moreover, the partial safety factor concept based on the structural reliability theory was also applied to the proposed collapse pressure estimation model, and, thus, the priority of importance of respective parameter constituting for the collapse of cylinders under external pressure was estimated in this study. From the application of the partial safety factor concept, the yield strength was concluded to be the most sensitive, and the initial ovality of tube was not so effective in the proposed collapse pressure estimation model. The present deterministic and probabilistic results are expected to be utilized in the design and maintenance of cylinders subjected to external pressure with initial ovality, such as the once-through type steam generator.

Quantification of Crack-Tip Constraint Effect on Master Curve Reference Temperature Based on Two-Parameter Approach

The master curve has evolved into a mature technology for characterizing the fracture toughness transition of ferritic steels. However, it is well known that the master curve reference temperature (To) values estimated from small laboratory specimen may be biased low due to loss of crack-tip constraint. To quantify such variations of To resulting from differences of crack-tip constraint of testing specimen, two-parameter fracture mechanics approaches are employed in the present study. In this context, fracture toughness test and 3-dimensional finite element (FE) analysis for several standard and nonstandard test specimens are performed to quantify relationship between variations of To and constraint parameters and to find best constraint parameter representing effect of crack-tip constraint on To values evidently. Based on testing and present FE results, To and constraint parameter loci are constructed and engineering To correlation models considering crack-tip constraint are suggested

Strain energy release rates for an interface crack in orthotropic media––a finite element investigation

Strain energy release rate (SERR) components for an interface crack in two-dimensional orthotropic media were obtained using finite element (FE) analysis. The elastic analysis of interface cracks results in oscillatory singularity. This is prevalent over a very small zone near the crack-tip, where the traction free crack faces undergo unacceptable deformations resulting in the interpenetration of crack faces. The individual and total strain energy release rates are calculated using modified crack closure integral (MCCI) method. Although the total SERR converges, it is observed that the individual SERR components are dependent on the values of the smallest element size (Δ a) at the crack-tip. It is observed that both the crack opening and sliding displacements are oscillatory when the interpenetration is allowed in the contact zone. The contact zone length ( r c) calculated using Suo's analytical expression [Singularities, interfaces and cracks in dissimilar anisotropic media. Proc. Royal Soc. London, Ser A427 (1990) 331] is in good agreement with the results from FE analysis and MCCI calculations. However, for the chosen material properties, the estimated contact zone length based on the analytical expression proposed by Ni and Nemat-Nasser [J. Mech. Phys. Solids 39 (1991) 113] exhibits a large deviation from the present FE results. It is seen that the mode-II behavior dominates the crack growth, even under mode-I loading.

Static strength variation of thick-walled CHS X-joints with different included angles and chord stress levels

This paper reports the results of numerical study on thick-walled circular hollow section (CHS) joints with inclined braces, including the axial chord stress effects on static joint strengths. Four brace inclination angles θ, varying from 30° to 90°, and three brace-to-chord diameter ratios β are considered. It was found that the sin θ term, frequently used in current design recommendation, is insufficient to account for the θ effect. Thin-walled and thick-walled joints exhibit different trends with respect to θ due to different stiffness of the chord wall which affects the stress distribution around the brace–chord intersection. The brace inclination angle is found to influence the load-transfer mechanism in the joint and consequently the interaction between the braces loads and chord stresses. A new chord stress function is proposed in this paper, with the geometric parameters θ and β incorporated, which shows good agreement with the present finite element results.

Approximate J estimates for tension-loaded plates with semi-elliptical surface cracks

This paper provides a simplified engineering J estimation method for semi-elliptical surface cracked plates in tension, based on the reference stress approach. Note that the essential element of the reference stress approach is the plastic limit load in the definition of the reference stress. However, for surface cracks, the definition of the limit load is ambiguous (“local” or “global” limit load), and thus the most relevant limit load (and thus reference stress) for the J estimation should be determined. In the present work, such limit load solution is found by comparing reference stress based J results with those from extensive 3-D finite element (FE) analyses. Based on the present FE results, the global limit load solution proposed by Goodall for surface cracked plates in combined bending and tension was modified, in the case of tension loading only, to account for a weak dependence on w/ c and was defined as the reference normalizing load. Validation of the proposed equation against FE J results based on actual experimental tensile data of a 304 stainless steel shows excellent agreements not only for the J values at the deepest point but also for those at an arbitrary point along the crack front, including at the surface point. Thus the present results provide a good engineering tool for elastic–plastic fracture analyses of surface cracked plates in tension.

Analysis of composite structures with distributed and localized damage by the finite-element method

A finite-element method of analysis is proposed for the analysis of composite laminates containing transverse cracks. The formulation is particularly simple as the effects of the damage are fully incorporated into the damage vector, which contains the set of internal state variables. Application of the finite-element code is demonstrated through examples of analysis of composite laminates with centrally located holes. Comparison with experimental stress-strain curves show good agreement with the present finite-element results. Furthermore, the finite-element analysis also enables the damage distribution maps to be obtained for each individual layer.

Postbuckling compressive strength of graphite/epoxy laminated cylindrical panels loaded in compression

The postbuckling compressive strength and collapse phenomena of composite laminated cylindrical panels with various fiber angles and width-to-length ratios are characterized by the nonlinear finite element method. For the iteration and load increment along the postbuckling equilibrium path, a modified arc-length method in which the effect of stress unloading due to failure can be considered is introduced. In the progressive failure analysis, the maximum stress criterion and complete unloading model are used. Validity of present finite element results are verified by experiment for [0 3 /90] S cylindrical panel and [0/90/±45] S plate. The postbuckling compressive strength of composite laminated cylindrical panels is independent of the initial buckling stress but high in the panel with large value of the bending stiffness in axial direction. In several of the cylindrical panels, it is observed that the prebuckling compressive failures occur and directly result in collapse before buckling.

Analysis of sandwich plates using a mixed finite element

The stress and displacement analysis of the thick sandwich plate is presented here by using an interlaminar stress mixed finite element based on local high-order deformable theory. The displacements of a sandwich plate are assumed to be high order polynomial functions layer-by-layer through the plate thickness. Since the interlaminar stresses at the interface between layers in this finite element scheme are regarded as primary variables, they can then be accurately determined. The accuracy of this finite element scheme is checked by comparing the present results with 3-D elasticity solutions of a simply supported sandwich plate. The response of a thick angle-ply, fiber-reinforced plastic (FRP) faced sandwich with fully simple supports, subjected to a sinusoidal distribution of transverse load is evaluated. The present finite element results are compared with results obtained from other finite element schemes.

Observations on bolted connections in composite structures

A three-dimensional finite element analysis of pin-loaded and bolted holes in (0/90) s and (90/0) s laminates has been performed. Through thickness clamping, pin-hole contact friction and laminate stiffness have been shown to contribute significantly to the resulting stress distributions. The importance of the clamping ratio, stacking sequence and clamping type are shown to have a fundamental influence on the magnitude of the interlaminar normal stress local to the bolt hole. Qualitative comparisons made with observed bearing failures in pin-loaded glass-reinforced polyester laminate specimens have given good agreement with the present finite element results.

Non-linear analysis of adhesively bonded joints

An updated Lagrangian formulation is used to develop a 2-D finite element for the analysis of adhesively bonded joints. The finite element accounts for the geometric non-linearity. The present finite element results are in good agreement with those reported in the literature. The effect of boundary conditions and mesh on the stress distributions in lap joints is also investigated.

Finite element flutter analysis of multi-web wing structures

The flutter analysis of multi-web aircraft wing structures is considered by using finite element idealization. The constant stress triangular membrane elements, the rectangular shear panels and the pin-jointed bar elements are used to idealize the wing structure. The order of the aerodynamic, mass and stiffness matrices of the assembled structure is reduced by introducing the first few natural modes of the structure as genenalized coordinates. The approach is quite general and is applicable to any multi-web wing structure with arbitrary configuration, which might have cutouts and other structural discontinuities. Three example wing structures are considered to illustrate the effectiveness of the approach and the present finite element results are found to be in good agreement with those given by other conventional methods.