Linear Finite Element Analysis Research Articles

Thermal-structural Modeling of power electronic package: effects of deposition geometry and dry spot on the stress distributions

A Power Electronics package is a heterogeneous system made of semiconductor devices (dies), metallic-ceramic substrate, baseplate and encapsulating material.The electronic devices can be MOSFETs (Metal Oxide Semiconductors Field Effect Transistors), diodes, IGBTs (Insulated Gate Bipolar Transistors) and passive components such as capacitors, resistors and sensors integrated on support circuit; the complete set of semiconductor devices installed on a package form the so-called “power modulus”.These devices play an important role in the transmission and conversion of energy in electric and hybrid vehicles. Due to the elevated currents and, consequently, the elevated temperatures at which these systems work, and due to the mismatch of the thermal-mechanical properties of the materials from which they are made, stresses and strains develop within the devices.Such stresses can be locally concentrated and amplified, depending on the deposition geometry of the various layers constituting the semiconductor device. Edge termination structures are essential to decrease the electric field at die’s edges, and, including brittle compounds in their composition, like Si3N4 or SiO, they are quite sensitive to mechanical stress.Another reason that may cause the stresses concentrations is the presence of dry spots. Dry spots are areas of various size, located at the interface between die or leadframe and the encapsulating resin, where there is a total or partial lack of adhesion.The aims of this work are, mainly, two. At first, four linear finite element analyses have been performed in order to evaluate the stresses concentrations at the corners of edge termination structure.The first case concerns sharp corners and the other cases concern differently filleted corners. In the second part of this work, it has been analysed the dry spot effect on stress distributions. Due to the small size of the defect with respect to the whole package, a Global-Local FEM approach has been used, creating a local subdomain where the mesh is denser than the global domain and a running a further separate numerical analysis which takes its boundary conditions from the global analysis, so delivering reliable small-scale stress and strain gradients. This approach permits to achieve accurate analyses focused on zones of interest of the global domain, limiting the increase of the computational cost of the modelling.

Repair Analysis of Overlay Woven Fabric CFRP Laminates

The increase in aerospace composites usage for structural components demands advanced repair analysis. Overlay repairs of carbon fiber-reinforced polymer laminates offer an alternative that is easier to perform and less time-consuming to produce than the widely used tapered scarf repair and stepped lap. Composite specimen manufacturing was based on both twill carbon/epoxy prepreg and wet lay-up. The repair was performed with both prepreg and wet extra plies to the parent prepreg structure. However, the design of overlay joints must be carefully investigated to avoid generating stress concentration regions at free edges. This study examined specific extra ply terminations' impact on peak stresses in the adhesive bond line. Linear finite element analysis was performed to conduct a maximum principal stress study with a focus on three joint design parameters: ply material, overply effect, and stacking sequence. FEA accurately predicted experimentally observed responses and provided further insight into the failure behavior of the structure. Results showed that overlay joints have a strong sensitivity to ply material type, the number of overply, and stacking sequence. The introduction of overplies provided protection and stiffness at joint tips, and an overply material behavior was identified. The location of 0̊ plies in the composite laminates was highlighted as an important factor. The analysis was then extended to three-dimensional FE models for verification. In conclusion, results showed that high-stress concentration in overlay joints can be mitigated with the introduction of overplies and appropriate changes in joint design parameters to reduce stress peaks at joint tips and corners.

Analysis of compliant mechanisms with series and parallel substructures through the ellipse of elasticity theory

Compliant mechanisms with complex hybrid configurations have been designed to meet the requirements of specific applications demanding high performance. Kinetostatic analysis, fundamental at the early stage of design, can become difficult for compliant systems characterized by series and parallel substructures. In the present paper, the ellipse of elasticity method is implemented for the analysis of a compliant mechanism with hybrid topology. Firstly, the ellipses associated to the different flexure hinges, characterized by uniform or non-uniform cross-sections, and by constant or variable initial curvature, are determined. Then, the unique ellipse representing the compliant mechanism is obtained by means of series and parallel compositions. By exploiting the antiprojective polarity properties of the ellipse, the kinetostatic analysis of the compliant system is reduced to a geometric problem with a straightforward solution. Linear and nonlinear finite element analyses and experimental tests are performed to verify the theoretical results.

Structural Performance of Large-Scale 3D-Printed Walls Subjected to Axial Compression Load

Despite the growing incorporation of additive manufacturing in the construction industry, a significant gap persists in the availability of design guidelines and comprehensive structural assessments for 3D-printed components. This research employs experimental methods to evaluate the performance of large-scale hollow unreinforced 3D-printed masonry walls under axial compressive load. Furthermore, a design methodology tailored for 3D-printed masonry walls under compressive loads is proposed in compliance with both American and Canadian masonry standards. This methodology is supported by the application of linear elastic 3D finite element analysis. Moreover, supplementary insights into material behavior are garnered through the examination of small specimens extracted from an additional 3D-printed wall. The results reveal that 3D printing reduces stiffness and compressive strength. The 3D-printed infills played an important role in redistributing stress after cracking. All full-scale 3D-printed masonry walls examined in this research exceeded the performance criteria set by the American masonry standard for load-bearing walls.

Study on Nanomaterials Coated Natural Coir Fibers as Crack Arrestor in Cement Composite

The process of inclusion of carbon nanotubes as fibers in cement paste has been proved to have optimistic effect as it enhances the tensile property of cement paste composite. Coir fibers have exceptional mechanical qualities and are thus employed as reinforcement in cement composites. Epoxy resin, which has a high Young’s modulus, is an ideal component for bonding carbon nanotubes (CNTs) to coir fiber. This paper describes a novel kind of nanocomposite made of L-12 epoxy resin and CNTs at the nanolevel, along with coir fibers at the microlevel which operate as crack arrestors. To remove surface contaminants, coir fibers are first treated with sodium hydroxide (NaOH). Epoxy/CNTs polymer coatings were developed at varying CNTs fractions (0.05, 0.1, 0.15, and 0.2 wt.% of cement). Multiwalled CNTs were combined in distilled water, followed by epoxy resin and hardener (9 : 1 v/v) polymer in an ultrasonic sonicator for 90 min to ensure full dispersion of CNTs within the epoxy polymer. This blend is now coated on the treated clustered coir fiber (length 10 cm, 10 strands) and reinforced along the length of a cement composite beam 20 mm × 20 mm × 80 mm in size. Tensile and three-point tests were performed to evaluate the mechanical characteristics of the hybrid composite. The linear elastic finite element analysis is employed to distinguish their failure phenomena via fatigue or fracture behavior. The microstructure behavior and the effect of coating material on the coir fibers were investigated using scanning electron microscope and EDX analysis. The reinforcing impact of nanopolymer coated coir fiber in cement composite diminished the tensile and flexural strength after 0.1 wt.% of CNT fraction but increased the composite’s durability and Young’s modulus. Fourier transform infrared spectroscopy analysis was carried out to assess the chemical interaction between the epoxy/CNTs and the coir fibers. The simulation was performed using ANSYS workbench, and the modeling results were within an acceptable 10% range of the experimental data. Nevertheless, it can be concluded that the hybrid composite is capable of enhancing the composite’s stress and strain capacity by regulating the fracture propagation process at the crack’s end.

Using the Point Method to estimate failure loads in 3D printed graphene-reinforced PLA notched plates

This work estimates failure loads in Fused Filament Fabrication (FFF) printed graphene-reinforced PLA (polylactic acid) plates containing different types of stress risers. With this aim, firstly, several notched plates are tested and conducted to fracture. Then, linear elastic Finite Element (FE) analyses are completed to define the corresponding stress profiles and, finally, the Point Method (PM) is applied to establish the failure criterion. This approach asserts that fracture conditions are achieved when the stress level equates the inherent strength (σ0) at a distance from the notch tip equal to L/2, so both parameters (related to each other through the material fracture toughness, Kmat) have been defined beforehand. The estimations of fracture loads obtained following this approach agree with the experimental results. Thus, the present work demonstrates the accuracy of the PM to estimate failure loads in this 3D printed material.

Feasibility of outrigger structural system for tall timber buildings: A numerical study

Tall timber buildings are prone to serviceability problems (e.g. lateral displacements and wind-induced accelerations). This article investigates the feasibility of timber outrigger system to build up to 20 storeys using linear elastic finite element analysis and relevant European and international standards such as EN 1990, EN 1991-1-1, EN 1991-1-4, EN 1995-1-1 and ISO 10137. The location of up to two outriggers was optimised based on different serviceability criteria. Various outrigger layouts were investigated, and their stiffness demands were discussed. The efficiency of outrigger structures in reducing lateral displacements and wind-induced accelerations is highlighted. A feasibility study considering serviceability requirements was performed using different basic wind velocities, number of storeys and gravity loads. Although the focus of the article is on serviceability requirements, some ultimate limit state considerations (forces and stresses) were briefly discussed. The results demonstrate the feasibility of building up to 16 storeys under medium to high wind velocities.

Study of Cyclic behaviour of Corroded HPC beams strengthened with GFRP laminates by Nonlinear finite element modelling and experimental investigations

Corrosion is a very big threat to the civil Engineering Structures especially on the coastal areas. Apart from the corrosion, the tidal forces on the structures act as the cyclic loading which in turn damage the structures by way of cyclic loading. There are two types of cyclic loading, which are constant amplitude and varying amplitude. In this experiment, cyclic loading was taken with Constant amplitude. Strengthening the corroded beams on tension face ie below the beams with GFRP laminates improve the cyclic life of the beams. In this paper, the non linear finite element analysis (ANSYS) for the corroded high performance concrete beams under cyclic loading to predict the cyclic life of the beams. The results were compared with the experimental results with regard to cyclic life and Maximum deflection. It is found that it is reasonably agreeable. This indicates that the proposed FEMs can capture the cyclic behavior of the corroded HPC beams strengthened with GFRC laminates of 2 different thicknesses of high accuracy.

Optimal mechanical properties of Hydroxyapatite gradient Voronoi porous scaffolds for bone applications — A numerical study

Irregular Voronoi-based lattice (IVL) structures in tissue engineering (TE) have significant potential for bone regeneration. These scaffolds can mimic natural human bone interconnectivity by gradually altering strut thickness (ST) and seed point space (PS), which affects both mechanical and biological characteristics. This paper investigates the impact of design parameters, ST and PS, on Hydroxyapatite (HA) ILV structures’ mechanical properties (elastic modulus (E) and maximum compressive strength (MCS)) and geometrical characteristics (pore number, size, and distribution, surface area (SA), and surface area-to-volume ratio (SA/VR)). Four types of IVL scaffolds were designed; PC-TC (Constant PS-Constant ST), PC-TG (Constant PS-Gradient ST), PG-TC (Gradient PS-Constant ST), and PG-TG (Gradient PS-Gradient ST). The study, conducted through linear static structural finite element analysis (FEA) with maximum stress criteria, underscores the profound impact of irregularity and morphology on mechanical performance and geometrical features. Regarding SA and SA/VR, a comparison between PC-TC with other proposed scaffolds showed a minor improvement for PC-TG, while higher significant improvements were found for both PG-TG and PG-TC. In terms of pores distribution and number, no noticeable improvement was observed for the PC-TG scaffold compared to PC-TC. In contrast, PG-TC and PG-TG lattices demonstrated a variety of pore distributions and approximately doubled pore numbers. Studying mechanical properties, considering E and MCS, showcases substantial gains for PG-TC. It, however, revealed that for the rest of the scaffolds, no enhancement was observed regarding E. Based on these results, gradient PS proved to be more effective than gradient ST in enhancing mechanical performance and geometrical properties. Due to these improvements, this study holds promise for expediting bone regeneration and reducing postoperative complications in bone replacement applications.

Structural evaluation of RC overhang cantilever slab strengthened with FRP near‐surface mounted (NSM) composites for bridge applications

AbstractThis paper presents the findings of a large‐scale experimental study that focus on assessing structural behavior of reinforced concrete (RC) cantilever slabs with carbon/epoxy fiber‐reinforced polymer (CFRP) composite strips using a near‐surface‐mounted (NSM) approach. The NSM/CFRP system evaluated in this study was implemented in strengthening the shoulders of the Slide Canyon Bridge in California, USA. The experimental phase is divided into two main parts: (i) determining the design parameters for NSM, including the bondline strength through pull‐out tests, and (ii) conducting a practical evaluation of the bending behavior of original and retrofitted RC cantilever slabs, each with varying NSM reinforcement and three different development lengths. Results of this study indicated that the use of NSM‐CFRP has a considerable benefit in that it significantly improves ductility and changes the failure mode of the unstrengthened RC slab from the typical brittle shear‐based failure mode to a more ductile flexural‐based failure mode. The large‐scale slab specimens' performances, which had different development lengths, showed little variance, except for the slab specimen with a development length of 457.0 mm that exhibited an appreciable flexural stiffness as compared to other specimens evaluated in this study. In order to simulate the serviceability and ultimate behavior of the RC slab specimens, linear and nonlinear finite element analyses were performed. A satisfactory agreement between numerical and experimental results was achieved especially at load level prior the initiation of large‐size cracks.

Design of a separator machine for oil palm fruit mesocarp and nut using computer‐aided design and linear finite element analysis

AbstractThis study addresses the inefficiencies in the current palm oil milling process, where the coexistence of mesocarp fiber and nut during pressing results in oil loss and nut breakage. To tackle this issue, the research aims to develop a machine that can separate mesocarp fibers from nuts before pressing, enhancing oil extraction and quality. The study involves designing the machine layout, creating schematic drawings, wireframe models, and assessing stress and deformation performance. Solidworks simulation was used to determine stress and deformation points within material properties, dimensions, and applied forces. The maximum stress on the rotating disc was 1.44 MPa, with a total deformation of 9.75 x 10−4 mm. Comparing this to the static component strength against cracking (0.093 MPa) revealed that the disc's material and design can safely with stand loads, preventing deformation during the mesocarp and nut separation process. This innovation promises to increase oil yields and improve oil quality in palm oil milling.Practical applicationsThe separation of mesocarp fiber and nuts using centrifugal force is a feasible method. By removing nuts from the mesh (fiber) prior digestion and oil extraction process, the issue of nut breakage will be completely omitted, and thus the pressure can be further increased to maximize oil yield at the palm oil mill industries. This suggested approach has been demonstrated to produce a large amount of oil with minimal broken kernels. The crude palm oil obtained from this separation process also satisfies industrial standards.

Protective potential of different mouthguard thicknesses against perianaesthetic dental trauma: a patient specific-finite element study

Perianaesthetic dental trauma is a common anaesthesia-related complication. Theprevious studies have shown a lack of knowledge regarding mouthguard usage and controversial results related to perianaesthetic dental trauma prevention. This study aimed to conduct a finite element analysis of the compressive and tensile stresses on the tooth-periodontal ligament-bone complex using custom-made mouthguards of different thicknesses and glass fibre splints to prevent perianaesthetic dental trauma. Custom-fitted ethylene-vinyl acetate mouthguards of two different thicknesses (2 and 3 mm) and glass fibre splint were modelled. A linear static finite element analysis was performed by applying a rigid Macintosh laryngoscope to the palatal surface of the maxillary central incisors at 150 N. The model without a mouthguard and glass fibre splint showed the highest stress values at the palatinal root surfaces during the impact. Increasing the mouthguard thickness significantly decreased the stress-strain values regardless of the presence of the glass fibre splint. Maximum stresses in the group using the 3 mm mouthguard were the lowest compared with the other groups.

Assessment of residual stresses in welded T-joints using contour method

Welded T-joints are commonly used in manufacturing of stiffened panels or crossbeams. However, welding of web-to-flange joint induces residual stresses and distortions resulting in significant challenges during both manufacturing and service. These issues can ultimately impact the structural performance, including fatigue and stability, and lifetime of the weldment. The purpose of current paper is determining the distribution and magnitude of manufacturing-induced longitudinal residual stresses in welded T-joints. Influence of hot rolling, thermal cutting, prestressing, welding, etc. are all included using the so-called contour method. Deformed surfaces are measured using coordinate measuring machine after wire electrical discharge machining of specimens. An inverse linear elastic finite element analysis is carried out for assessing residual stresses after data smoothing. Two-dimensional longitudinal residual stress patterns are evaluated in representative cross-sections clearly indicating high stress peaks near the welds, even exceeding yield strength of the base material. In addition, longitudinal membrane residual stresses are determined based on through-thickness stresses. In addition, a simplified residual stress model, satisfying the requirement for equilibrium of internal forces and bending moments, is developed for welded T-joints with double-sided fillet welds based on contour method results.

Investigation of anchorage plate opening on bursting force

Three-dimensional (3D) Finite Element analyses were performed to investigate transverse stresses and bursting forces at the anchorage zone in post-tensioned concrete beams. The behavior of the concrete beam was investigated through linear elastic Finite Element analyses. To validate the Numerical modeling results, an experimental study was performed on a beam and results are compared in terms of ultimate strength. The effect of duct hole and eccentricity are investigated by varying diameter and eccentric distances on the concrete beam. Furthermore, the results are validated for bursting stress and bursting force. Altogether, the equation of bursting force in IS 1343:2012 hasn’t considered the effect of duct hole and eccentricity, the results are compared with IS 1343:2012, and an equation is presented considering the effect of duct and eccentricity.

A numerical study on stress mitigation in through-thickness tailored bi-adhesive single-lap joints

In bi-adhesive single-lap joints (SLJs), longitudinal grading of adhesive compliance leads to peak stress concentration to the bi-adhesive interface (due to mismatch in properties). Due to this additional stress concentration at the bi-adhesive interface, the failure initiation threshold is lowered. In this paper, the stress distribution in the compliance-tailored bi-adhesive joints is investigated numerically. Peak stress at the bi-adhesive interface is diffused by geometrically grading the bi-adhesive interface in the longitudinal and transverse (through the thickness) directions. Linear and non-linear (material and geometric) finite element (FE) analyses were performed for two different set of bi-adhesive bondlines and joint configurations. FE results were benchmarked with published experimental and numerical data. Peak peel stress and peak shear stress are decreased by 29–70% and 8%, respectively, when the bi-adhesive interface is graded geometrically in the transverse and longitudinal directions as opposed to longitudinal tailoring alone. Moreover, the bi-adhesive interface’s stress concentration is reduced significantly. This leads to a more homogeneous stress distribution throughout the bond-layer. A thorough investigation reveals that through-thickness compliance tailoring of the bi-adhesive in SLJ can be used to increase tolerance to high load levels, achieve uniform stress distribution along the bond-layer, and reach the optimum joint stiffness.HighlightsA new approach for stress mitigation involving through the thickness tailoring of adhesive is introducedProposed approach is validated for two sets of bi-adhesive systems and two joint configurationsFinite element results are validated with published experimental dataLoad carrying capacity of joints is enhanced by diffusing peak stresses away from the bi-adhesive interface

Relative Effects of Radiation-Induced Changes in Bone Mass, Structure, and Tissue Material on Vertebral Strength in a Rat Model.

The observed increased risk of fracture after cancer radiation therapy is presumably due to a radiation-induced reduction in whole-bone strength. However, the mechanisms for impaired strength remain unclear, as the increased fracture risk is not fully explained by changes in bone mass. To provide insight, a small animal model was used to determine how much of this whole-bone weakening effect for the spine is attributable to changes in bone mass, structure, and material properties of the bone tissue and their relative effects. Further, because women have a greater risk of fracture after radiation therapy than men, we investigated if sex had a significant influence on bone's response to irradiation. Fractionated in vivo irradiation (10 × 3 Gy) or sham irradiation (0 Gy) was administered daily to the lumbar spine in twenty-seven 17-week-old Sprague-Dawley rats (n = 6-7/sex/group). Twelve weeks after final treatment, animals were euthanized, and lumbar vertebrae (L4 and L5 ) were isolated. Using a combination of biomechanical testing, micro-CT-based finite element analysis, and statistical regression analysis, we separated out the effect of mass, structural, and tissue material changes on vertebral strength. Compared with the sham group (mean ± SD strength = 420 ± 88 N), the mean strength of the irradiated group was lower by 28% (117 N/420 N, p < 0.0001). Overall, the response of treatment did not differ with sex. By combining results from both general linear regression and finite element analyses, we calculated that mean changes in bone mass, structure, and material properties of the bone tissue accounted for 56% (66 N/117 N), 20% (23 N/117 N), and 24% (28 N/117 N), respectively, of the overall change in strength. As such, these results provide insight into why an elevated clinical fracture risk for patients undergoing radiation therapy is not well explained by changes in bone mass alone. © 2023 The Authors. Journal of Bone and Mineral Research published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research (ASBMR).

Mechanical demands of bite in plane head shapes of ant (Hymenoptera: Formicidae) workers

AbstractFood processing can exert significant evolutionary pressures on the morphological evolution of animal appendages. The ant genus Pheidole displays a remarkable degree of morphological differentiation and task specialization among its workers. Notably, there is considerable variation in head shape within worker subcastes of Pheidole, which could affect the stress patterns generated by bite‐related muscle contraction. In this study, we use finite element analysis (FEA) to investigate the effect of the variation in head plane shape in stress patterns, while exploring the morphospace of Pheidole worker head shapes. We hypothesize that the plane head shapes of majors are optimized for dealing with stronger bites. Furthermore, we expect that plane head shapes at the edges of each morphospace would exhibit mechanical limitations that prevent further expansion of the occupied morphospace. We vectorized five head shapes for each Pheidole worker type located at the center and edges of the corresponding morphospaces. We conducted linear static FEA to analyze the stresses generated by mandibular closing muscle contraction. Our findings indicate that plane head shapes of majors exhibit signs of optimization to deal with stronger bites. Stresses are distinctly directed along the lateral margins of the head, following the direction of muscle contraction, whereas the stresses on the plane head shapes of minors tend to concentrate around the mandibular articulations. However, the comparatively higher stress levels observed on majors' plane head shapes suggest a demand for cuticular reinforcement, like increased cuticle thickness or sculpturing pattern. Our results align with the expectations regarding the main colony tasks performed by each worker subcaste, and we find evidence of biomechanical limitations on extreme plane head shapes for majors and minors.

Data-driven artificial neural network for elastic plastic stress and strain computation for notched bodies

An integration of artificial neural network (ANN) and finite element (FE) analysis was developed to predict elastic–plastic stress and strains at notch locations based on a linear elastic FE analysis solution. Two FE models were created for different materials and multiaxial load cases to produce hypothetical elastic and elastic–plastic stress and strain datasets. One model was based on an elastic state, and the other was based on an elastic–plastic state. The ANN was trained with the elastic stress data from the linear elastic FE model as input and the elastic–plastic stress–strain data from the nonlinear elastic–plastic FE model as output. The dataset was divided into three groups: training, verification, and testing data. The ANN was trained using the training data, evaluated using the verification data, and tested for generalizability using the testing data. The results showed that the proposed methodology can predict elastic–plastic stress and strain fields for notched bodies under multiaxial loadings accurately and efficiently using only the elastic FE analysis solution.

A linear elastic finite element approach to fatigue life estimation for defect laden materials

This work assumed that the stress-life behaviors of defect-laden materials converge at a certain low life cycle and attempted to estimate fatigue life by applying relative knock-downs to the endurance limit of a reference stress-life data. Linear elastic finite element analysis on small cracks initiated from defects was performed to evaluate the effect of defect size, aspect ratio, and location on endurance limit. While for internal defects size and shape are both influential, size and depth were found to be more important for surface defects. These findings were validated against the fatigue lives of laser powder bed fused Ti-6Al-4V specimens.

An investigation into curved beam flange efficiency in thin-walled structure

Allowing a structural member to reach its full loading potential is likely the primary focus of structural analysis. Structural area that is ineffective is seen as ’parasitic’, and is eliminated either in the final design iteration, or in a subsequent weight-optimization exercise. Curved beam flange efficiency is the term used to refer to the outstanding flange of a beam, curved in the plane of bending, that is subjected to uniaxial bending along its principal axis. The seminal research articles outlining the phenomenon of curved beam flange efficiency were written in the 1950s; as outlined in a comprehensive literature review herein. These articles shed light on a phenomenon that, to an extent, remains enigmatic amongst structural engineers. Graphs based on seemingly complicated equations are advocated in aircraft structural directives; yet the fundamental mechanism of the true axial stress distribution in an outstanding curved beam flange remains elusive. It is the purpose of the proposed investigation to highlight some aspects of the phenomenon that, as yet, have not received adequate attention through rigorous analysis. Furthermore, relatively ’simple’ linear Finite Element analysis, validated by the aforementioned fundamental research, is shown to adequately capture the phenomenon. Finally, a method is proposed that considers the influence of the corner fillet radius at the connection of the flange to the web, a detail that has not been fully investigated in the literature. The method is outlined for a C section, but can be applied to all thin-walled sections (Z, I and T). The proposed method shows good correlation with current methods found in the literature (for no fillet radius). By fully exploiting the increased stiffness afforded by the corner fillet radius, as well as the concomitant reduction of material, the proposed method, validated by FE analysis, ’recovers’ some of the efficiency ’lost’ by the flange.