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Full-Text Articles in Engineering

Experimental And Computational Analysis Of Progressive Failure In Bolted Hybrid Composite Joints, John S. Brewer Dec 2020

Experimental And Computational Analysis Of Progressive Failure In Bolted Hybrid Composite Joints, John S. Brewer

Theses and Dissertations

Composite materials are strong, lightweight, and stiff making them desirable in aerospace applications. However, a practical issue arises with composites in that they behave unpredictably in bolted joints, where damage and cracks are often initiated. This research investigated a solution to correcting the problem with composite bolted joints. A novel hybrid composite material was developed, where thin stainless steel foils were placed between and in place of preimpregnated composite plies during the cure cycle to reinforce stress concentrations in bolted joints. This novel composite was compared to control samples experimentally in quasi-static monotonic loading in double shear configuration in 9-ply …


Modeling Hybrid Composites Using Tsai-Wu And Hashin Failure Criterion, Candice R. Roberts Mar 2020

Modeling Hybrid Composites Using Tsai-Wu And Hashin Failure Criterion, Candice R. Roberts

Theses and Dissertations

Hybrid composites require further study and testing for future use in various fields. This study focuses on simulating a Hybrid Composite using IM7-977-3 laminae with steel foils in Abaqus under bolt loading by using Hashin and Tsai-Wu failure criterion. Initial simulations contain only the IM7-977-3 composite with cohesive layers. Foil samples were then tested for accurate material properties from which the simulations were then updated to include steel foils. The two models show that Tsai-Wu failure criterion, while great for anisotropic material in tension, does not prove accuracy around the hole of the composite material which is in compression. Hashin …


Mechanical Properties And Fatigue Behavior Of Unitized Composite Airframe Structures At Elevated Temperature, Mohamed Noomen Sep 2016

Mechanical Properties And Fatigue Behavior Of Unitized Composite Airframe Structures At Elevated Temperature, Mohamed Noomen

Theses and Dissertations

The tension-tension fatigue behavior of a newly developed unitized composite material system was investigated. The unitized composite consisted of a polymer matrix composite (PMC) co-cured with a ceramic matrix composite (CMC). The PMC portion consisted of an NRPE high-temperature polyimide matrix reinforced with carbon fibers woven in an eight harness satin weave (8HSW). The CMC layer is a single-ply non-crimp 3D orthogonal weave composite consisting of ceramic matrix reinforced with glass fibers. In order to assess the performance and suitability of this composite for use in aerospace components designed to contain high-temperature environments, mechanical tests were performed under temperature conditions …


Creep Of Sylramic-Ibn Fiber Tows At Elevated Temperature In Air And In Silicic Acid-Saturated Steam, Kevin B. Sprinkle Jun 2015

Creep Of Sylramic-Ibn Fiber Tows At Elevated Temperature In Air And In Silicic Acid-Saturated Steam, Kevin B. Sprinkle

Theses and Dissertations

Stressed oxidation experiments on Sylramic-iBN fiber tows were performed to evaluate the novel fiber's mechanical performance, creep behavior, and creep mechanisms. This research effort investigated creep response of Sylramic-iBN fiber tows at elevated temperatures in both air and in silicic acid-saturated steam environments. Creep experiments were conducted at creep stresses ranging from 127 to 762 MPa at 400°C and 500°C in order to examine the mechanical behavior of the Sylramic-iBN fiber tows at temperatures below and above the melting point of boria (450°C). Sylramic-iBN fibers are known to have excellent creep resistance, better than most other non-oxide fibers and significantly …


Effect Of Prior Exposure At Elevated Temperatures On Tensile Properties And Stress-Strain Behavior Of Three Oxide/Oxide Ceramic Matrix Composites, Christopher J. Hull Mar 2015

Effect Of Prior Exposure At Elevated Temperatures On Tensile Properties And Stress-Strain Behavior Of Three Oxide/Oxide Ceramic Matrix Composites, Christopher J. Hull

Theses and Dissertations

Thermal stability of three oxide-oxide ceramic matrix composites was studied. The materials studied were NextelTM610/aluminosilicate (N610/AS), NextelTM720/aluminosilicate (N720/AS), and NextelTM720/Alumina (N720/A), commercially available oxide-oxide ceramic composites (COI Ceramics, San Diego, CA). The N610/AS composite consists of a porous aluminosilicate matrix reinforced with laminated woven alumina N610 fibers. The N720/AS and N720/A composites consist of a porous oxide matrix reinforced with laminated, woven mullite/alumina (NextelTM720) fibers. The matrix materials are aluminosilicate in N720/AS and alumina in N720/A. All three composites have no interface between the fibers and matrix, and rely on the porous …


Fatigue Behavior Of Im7/Bmi 5250-4 Composite At Room And Elevated Temperatures, James T. Tipton Mar 2015

Fatigue Behavior Of Im7/Bmi 5250-4 Composite At Room And Elevated Temperatures, James T. Tipton

Theses and Dissertations

The tension-tension fatigue and tension-compression fatigue behaviors of the IM7/BMI 5250-4 composite were investigated. The tension-tension fatigue of the composite with 0/90 and ±45 fiber orientations was studied at 23, 170, and 190°C. The tension-compression fatigue of the composite with 0/90 fiber orientation was examined at 23°C. The tensile and compressive properties of the composite were also evaluated at room and elevated temperatures for both 0/90 and ±45 fiber orientations. Elevated temperature had little effect on the tensile properties of the 0/90 fiber orientation, but strongly influenced the ±45 tensile properties as well as the compressive properties of both fiber …


Tension-Compression Fatigue Of An Oxide/Oxide Ceramic Matrix Composite At Elevated Temperature In Air And Steam Environments, Richard L. Lanser Mar 2015

Tension-Compression Fatigue Of An Oxide/Oxide Ceramic Matrix Composite At Elevated Temperature In Air And Steam Environments, Richard L. Lanser

Theses and Dissertations

Tension-compression fatigue behavior of an oxide-oxide ceramic matrix composite was investigated at 1200°C in air and steam. The composite is comprised of an alumina matrix reinforced with Nextel 720 fibers woven in an eight harness satin weave. The composite relies on a porous matrix for damage tolerance. Compression and tension tests to failure were conducted to characterize basic mechanical properties. Tension-compression fatigue tests were performed at 1 Hz frequency with a ratio of minimum to maximum stress of -1. Maximum stresses ranged from 60-120 MPa. Fatigue run-out (defined as 105 cycles) was achieved in air at 80 MPa and in …


Structural Health Monitoring Of M1114 High Mobility Multipurpose Wheeled Vehicle Armor System, Frank T. Sha Mar 2012

Structural Health Monitoring Of M1114 High Mobility Multipurpose Wheeled Vehicle Armor System, Frank T. Sha

Theses and Dissertations

The M1114 High Mobility Multipurpose Wheeled Vehicle (HMMWV) has been the workhorse vehicle of the U.S. Armed Forces in Afghanistan and Iraq. Donald Rumsfeld, Secretary of Defense, was faced with massive public criticism in 2004 for not equipping our military personnel in Afghanistan and Iraq with M1114s that had the proper ballistic armor. In May 2004, a $618M Senate Bill was passed to increase the production level of HMMWVs and improve their ballistic protection capabilities while minimizing additional weight. While the military is taking advantage of using composite armor on the HMMWV, it does not have a rigorous method to …


Creep Behavior In Interlaminar Shear Of A Cvi Sic/Sic Composite At Elevated Temperatures In Air And Steam, Matthew T. Pope Mar 2012

Creep Behavior In Interlaminar Shear Of A Cvi Sic/Sic Composite At Elevated Temperatures In Air And Steam, Matthew T. Pope

Theses and Dissertations

This research investigated the interlaminar shear performance of a SiC/SiC ceramic matrix composite. The interlaminar shear performance was observed in compression of double notched specimens (DNS) at 1200°C in both laboratory air and in steam. Compression to failure tests determined the as-processed interlaminar shear strength and interlaminar shear creep tests were conducted with stresses ranging from -22 MPa to -16 MPa. Primary and secondary creep regimes were observed in all creep tests. The specimens tested in creep at -16 MPa in air achieved run-out, defined as 100 hours at creep stress. The residual strength decreased slightly after 100 h of …


Part Count: Monolithic Part Effects On Manufacturing Labor Cost, An Aircraft Applied Model, Aaron M. Lemke Mar 2010

Part Count: Monolithic Part Effects On Manufacturing Labor Cost, An Aircraft Applied Model, Aaron M. Lemke

Theses and Dissertations

There are significantly different manufacturing processes and part counts associated with composites that are not currently addressed within the aircraft procurement and life cycle management processes in the Department of Defense (DoD). A series of affordability initiatives have culminated in significant evidence over the last decade to better quantify the impact of primarily composite structures in aircraft. An Air Force Research Laboratory program, Advanced Composite Cargo Aircraft (ACCA), provides substantial support for the impact of part size on life cycle cost for payload aircraft. This research evaluates select methods used and seeks to introduce modifications to the projected manufacturing hours …


Mechanical Properties Characterization And Business Case Analysis Of The Fiber Metal Laminate Glare-3 For Use As Secondary Aircraft Structure, Benjamin O. Elton Mar 2010

Mechanical Properties Characterization And Business Case Analysis Of The Fiber Metal Laminate Glare-3 For Use As Secondary Aircraft Structure, Benjamin O. Elton

Theses and Dissertations

This effort explored the mechanical characteristics and economic feasibility of using the fiber metal laminate, GLARE-3, as a secondary aircraft structure; specifically, the cargo floor of a C-130. The mechanical properties were determined through static four-point bending and tensile testing and dynamic impact testing. Aggregate behavior of the constituent materials was predicted using a model which consisted of Mass Volume Fraction (MVF) and Classical Laminated Plate Theory (CLPT) methods using known values for the constituents. Static testing was conducted on coupon-level specimens using standardized testing procedures. Static tensile tests were conducted on specimens with four different fiber orientations, 0°, 22.5°, …


Fatigue Behavior Of An Advanced Sic/Sic Composite At Elevated Temperature In Air And In Steam, Devon T. Christensen Dec 2009

Fatigue Behavior Of An Advanced Sic/Sic Composite At Elevated Temperature In Air And In Steam, Devon T. Christensen

Theses and Dissertations

The fatigue behavior of an advanced Silicon Carbide/Silicon Carbide (SiC/SiC) ceramic matrix composite (CMC) was investigated at 1200 ˚C in laboratory air and in steam environments. The composite consisted of a SiC matrix reinforced with Boron Nitride (BN) coated Hi-Nicalon fibers woven into eight-harness-satin (8HS) weave plies. Tensile stress-strain behavior and tensile properties were also evaluated at 1200 ˚C. Tension-tension fatigue tests were conducted in both laboratory air and in steam at 1200 ˚C at frequencies of 0.1 Hz, 1.0 Hz, and 10 Hz. The tension-tension fatigue tests had a ratio of minimum stress to maximum stress of R = …


Fatigue Evaluation Of Nanocomposites As Lightweight Electronic Enclosures For Satellites' Applications, Javier Rodriguez Mar 2009

Fatigue Evaluation Of Nanocomposites As Lightweight Electronic Enclosures For Satellites' Applications, Javier Rodriguez

Theses and Dissertations

Existing nanocomposite materials used for satellite applications don't offer the required conductivity and electromagnetic shielding protection, requiring metal shields in order to survive in space. The AFRL Materials and Manufacturing Directorate in conjunction with the private sector have developed a material that promises to blend the attributes of nanocomposites and metal materials. The M55J/RS3 material consists of carbon fibers combined with a polyisocyanate matrix, in which Nickel nanostrandsTM are added. The research effort investigated the changes in the EMI and ESD of the material after being subjected to cyclic loads. Four configurations of a symmetric layup with fibers oriented …


Nondestructive Evaluation Of Aircraft Composites Using Terahertz Time Domain Spectroscopy, Christopher D. Stoik Dec 2008

Nondestructive Evaluation Of Aircraft Composites Using Terahertz Time Domain Spectroscopy, Christopher D. Stoik

Theses and Dissertations

Terahertz (THz) time domain spectroscopy (TDS) was assessed as a nondestructive evaluation technique for aircraft composites. Material properties of glass fiber composite were measured using both transmission and reflection configuration. The interaction of THz with a glass fiber composite was then analyzed, including the effects of scattering, absorption, and the index of refraction, as well as effective medium approximations. THz TDS, in both transmission and reflection configuration, was used to study composite damage, including voids, delaminations, mechanical damage, and heat damage. Measurement of the material properties on samples with localized heat damage showed that burning did not change the refractive …


A Novel Method Characterizing The Impact Response Of Functionally Graded Plates, Reid A. Larson Sep 2008

A Novel Method Characterizing The Impact Response Of Functionally Graded Plates, Reid A. Larson

Theses and Dissertations

Functionally graded material (FGM) plates are advanced composites with properties that vary continuously through the thickness of the plate. Metal-ceramic FGM plates have been proposed for use in thermal protection systems where a metal-rich interior surface of the plate gradually transitions to a ceramic-rich exterior surface of the plate. The ability of FGMs to resist impact loads must be demonstrated before using them in high-temperature environments in service. This dissertation presents a novel technique by which the impact response of FGM plates is characterized for low-velocity, low- to medium-energy impact loads. An experiment was designed where strain histories in FGM …


Hall Thruster Plume Diagnostics Utilizing Microwave Interferometry, Vipul Sharma Sep 2008

Hall Thruster Plume Diagnostics Utilizing Microwave Interferometry, Vipul Sharma

Theses and Dissertations

The fatigue behavior of two woven SiC-SiNC ceramic matrix composites (CMCs) was investigated at 1300 °C in laboratory air and in steam. The first composite (C1) consists of a PIP SiNC matrix reinforced with Sylramic (Syl) fibers woven in a five-harness satin weave fabric and coated with a proprietary dual-layer interface. The second composite (C2) consists of a modified PIP SiNC matrix reinforced with Sylramic-iBN (Syl-iBN) fibers woven in a five-harness satin weave fabric and coated with a proprietary dual-layer interface. The tensile stress-strain behavior was investigated and the tensile properties measured at 1300°C. Tension-tension fatigue behavior was studied for …


Analysis Of Multi-Layered Materials Under High Velocity Impact Using Cth, Jason K. Lee Mar 2008

Analysis Of Multi-Layered Materials Under High Velocity Impact Using Cth, Jason K. Lee

Theses and Dissertations

Multi-layer armor containing ceramic and metallic layers has become more common in the past two decades. Typically, ceramics have high compressive strength which combined with their low density make them highly desirable for armor applications. This research effort numerically simulates high velocity impact of cylindrical projectiles on multi-layer metallic and ceramic targets of finite thickness. The impact of the projectile occurs normal to the surface of the target. The projectiles used are made of either S7 tool steel or tungsten. The targets consist of either rolled homogeneous armor, 4340 steel and boron carbide ceramic or rolled homogeneous armor and boron …


Effects Of Environment On Creep Behavior Of Nextel 720/Alumina-Mullite Ceramic Composite At 1200°C, Christopher L. Genelin Mar 2008

Effects Of Environment On Creep Behavior Of Nextel 720/Alumina-Mullite Ceramic Composite At 1200°C, Christopher L. Genelin

Theses and Dissertations

The creep behavior of an oxide-oxide ceramic matrix composite (CMC) was investigated at 1200°C in laboratory air, in steam and in argon. The composite consisted of a porous alumina-mullite matrix reinforced with laminated, woven mullite/alumina (Nextel/720) fibers. The composite had no fiber coating and relied on its porous alumina/mullite matrix for flaw tolerance. Tensile stress-strain behavior was investigated and the tensile properties were measured at 1200°C in laboratory air. Tensile creep behavior of the CMC was examined for creep stress levels of 73, 91, 114 and 136 MPa. Creep run-out, set to 100 h, was achieved for stress levels ≤ …


Modeling Fracture In Z-Pinned Composite Co-Cured Laminates Using Smeared Properties And Cohesive Elements In Dyna3d, Jason K. Freels Sep 2006

Modeling Fracture In Z-Pinned Composite Co-Cured Laminates Using Smeared Properties And Cohesive Elements In Dyna3d, Jason K. Freels

Theses and Dissertations

The purpose of the present research was three-fold: 1) gain a more sophisticated understanding of the response of co-cured composite joints with and without through-thickness reinforcement (TTR), 2) compare the behavior of specimens reinforced with various sizes and densities of reinforcement, and 3) use experimental data to verify the existing DYNA3D smeared property model. Double cantilever beam, end-notch flexure and T-section specimens reinforced with 0.011" diameter z-pins at 2% and 4% volume densities were tested to determine the mode I, mode II and mixed mode (I and II) behavior. Results were added to preliminary research in which tests were conducted …


Some Aspects Of The Mechanical Response Of Pmr-15 Neat Resin At 288°C: Experiment And Modeling, Christina M. Falcone Sep 2006

Some Aspects Of The Mechanical Response Of Pmr-15 Neat Resin At 288°C: Experiment And Modeling, Christina M. Falcone

Theses and Dissertations

The mechanical response of PMR-15 neat resin was investigated at 288?C. Monotonic loading/unloading tests performed at several constant stress rates revealed considerable rate dependence, especially on the unloading path. Effect of prior stress rate on creep behavior was evaluated in creep tests preceded by uninterrupted loading to a target stress. Creep response was dependent on the prior stress rate. Effect of loading history was studied in stepwise creep tests, where specimens were subjected to a constant stress rate loading followed by unloading to zero stress with intermittent creep periods during both loading and unloading. Comparison of creep strains accumulated during …


Creep-Rupture And Fatigue Behaviors Of Notched Oxide/Oxide Ceramic Matrix Composite At Elevated Temperature, Mark A. Sullivan Mar 2006

Creep-Rupture And Fatigue Behaviors Of Notched Oxide/Oxide Ceramic Matrix Composite At Elevated Temperature, Mark A. Sullivan

Theses and Dissertations

Oxide/oxide composites are being considered for use in high temperature aerospace applications where their inherent resistance to oxidation provides for better long life properties at high temperature than most other ceramic matrix composites (CMCs). One promising oxide/oxide CMC is Nextel 720/A (N720/A) which uses an 8-harness satin weave (8HSW) of Nextel 720 fibers embedded in a porous alumina matrix. Possible aerospace applications for N720/A will likely require inserting holes into the material for mounting and cooling purposes. The notch characteristics must be understood to ensure designs using the material are sufficient for the desired application. This research effort examined the …


Application Of Spline Variational Analysis Method In The Modeling Of Composite Repairs, Brian M. Fredrickson Mar 2006

Application Of Spline Variational Analysis Method In The Modeling Of Composite Repairs, Brian M. Fredrickson

Theses and Dissertations

The purpose of this thesis is to apply a non-commercialized spline-based (BSpline Analysis Method or BSAM) computer program to model and predict strain fields in two composite repairs, a scarf joint and a stepped-lap joint, subjected to static tensile loading. Test specimens with scarf and stepped-lap joints are fabricated using quasiisotropic sixteen ply panels made from IM6/3501-6 prepreg with a [+452/02/-452/902]s lay-up. The panels were bonded together with FM-300M (0.05psf), a 176°C cure film adhesive, under positive pressure. A total of five coupons of each joint type are made. Two of …


Characterization Of Functionally Graded Materials, Benjamin D. Chapman Mar 2006

Characterization Of Functionally Graded Materials, Benjamin D. Chapman

Theses and Dissertations

The purpose of this study was to characterize the behavior of a functionally graded material through experimentation and analytical modeling. Functionally graded materials are a ceramic metal composite which transitions from metal on one face to ceramic on the opposite face. Creating reliable models required verifying the material properties. This was accomplished through the use of a static modulus of elasticity test as well as a dynamic ping test. The natural frequencies from the dynamic test were compared with finite element models to determine which material properties most accurately represented the functionally graded material. It was found that the material …


Creep Behavior Of An Oxide/Oxide Composite With Monazite Coating At Elevated Temperatures, Sean S. Musil Mar 2005

Creep Behavior Of An Oxide/Oxide Composite With Monazite Coating At Elevated Temperatures, Sean S. Musil

Theses and Dissertations

This study focuses on experimental investigation of stress-rupture behavior (creep response) of an oxide/oxide composite in a cross-ply (0/90) lay-up at elevated temperature. The test material, Nextel 610/monazite/alumina composite, employs monazite, an oxidation-resistant interfacial coating designed to improve performance at elevated temperatures. The experimental program included monotonic tensile tests to failure and creep-rupture tests at elevated temperatures. Tensile tests served to establish an ultimate tensile strength (UTS) for the material. The ensuing creep-rupture tests involved stress levels at varying percentages of the UTS. Stress-rupture curves at 900 and 1100 degrees C were established. A family of creep curves for various …


Experimentation And Analysis Of Composite Scarf Joint, Benjamin M. Cook Mar 2005

Experimentation And Analysis Of Composite Scarf Joint, Benjamin M. Cook

Theses and Dissertations

Composite bonded scarf repairs were examined by experimentally measuring and analytically predicting the residual curing strains and strains due to mechanical loading. To accomplish this a three prong approach was used: a full strain field through a repaired laminate's thickness was measured for both a loaded specimen and a specimen with the residual strain released, models were developed for comparison to both states, and data was collected for large tensile test specimens at various stages of being scarf repaired. A ~14:1 straight scarfed one-inch wide specimen was used to collect Moire interferometry data to calculate a full strain field due …


Reduction Of Thermal Residual Strains In Adhesively Bonded Composite Repairs, Heather R. Crooks Mar 2003

Reduction Of Thermal Residual Strains In Adhesively Bonded Composite Repairs, Heather R. Crooks

Theses and Dissertations

Many military and commercial aircraft are being called upon to fly well beyond their original intended service lives. This has forced the United States Air Force (USAF) to increasingly rely on structural repairs to address fatigue induced damage and to extend aircraft useful life. The focus of this research is the use of a high-strength composite patch technique to repair a fatigue crack on an aluminum aircraft structure. This study investigates the thermal residual strains that occur as a direct result of the coefficient of thermal expansion (CTE) mismatch between the repair patch and the underlying cracked metallic structure to …


Mechanics Of A Functionally-Graded Titanium Matrix Composite, G. Brandt Miller Mar 2000

Mechanics Of A Functionally-Graded Titanium Matrix Composite, G. Brandt Miller

Theses and Dissertations

Functionally-graded Titanium Matrix Composites, (F/G TMCs) combine the ideal properties of titanium matrix composites with the more practical machining qualities of monolithic (unreinforced) alloy. This material shows great promise in application to aerospace structural components - even in parts whose design requirements have defied the use of composite materials in the past. Successful implementation of such a material would lead to enhanced aircraft performance. However, the basic properties of a functionally-graded titanium matrix composite need to be investigated. The composite/alloy transition region, or joint area, may be less strong than its constituents and therefore determine the overall performance of the …


Progressive Failure Analysis Of Composite Panels, Stephen M. Spottswood Mar 1999

Progressive Failure Analysis Of Composite Panels, Stephen M. Spottswood

Theses and Dissertations

The objective of this research was to determine the physical response, including material failure, of a curved composite panel designed to resist transverse loading. The cause of the material failure, in the form of delamination, fiber and/or matrix failure, was determined through various criterion based on non-linear movement using a finite element analysis technique. Data generated both with and without the addition of progressive failure criteria, was compared with previously published experimental data, noting where the theory diverges from the experimental results. The inclusion of various failure criterion, to include maximum stress, Lee, and Hashin, provided a more realistic representation …


Fatigue Response Of Repaired Thick Aluminum Panels With Bondline Flaws, David S. Conley Mar 1999

Fatigue Response Of Repaired Thick Aluminum Panels With Bondline Flaws, David S. Conley

Theses and Dissertations

his research investigated the fatigue response of precracked 558 x 177.8 x 6.35 mm (22.0 x 7.0 x 0.25 in) 2024-T351 aluminum panels repaired with single-sided partially bonded, unidirectional, eighteen ply boron/epoxy reinforcements. Disbonds were introduced into the bondline of each repair during the adhesion process using teflon inserts. Five different disbond configurations, with varying disbond locations and sizes, were tested. Each repaired panel was subjected to constant amplitude cyclic fatigue loading with a maximum stress of 120MPa. Results from the different configurations were compared against one another and against repaired panels with no debonds to assess the effect of …


Nonlinear Geometric And Material Behavior Of Composite Shells With Large Strains, Scott A. Schimmels Aug 1995

Nonlinear Geometric And Material Behavior Of Composite Shells With Large Strains, Scott A. Schimmels

Theses and Dissertations

A two-dimensional, geometrically and materially nonlinear shell theory applicable to arbitrary geometries described by orthogonal curvilinear coordinates and encompassing large displacements, moderate rotations for large strain situations has been developed. Additionally, the theory includes Jacobian transformation matrices, based upon displacement parameters, for the Cauchy - 2nd Piola-Kirchhoff stress-state and the Cauchy (Almansi) - Green strain-state transformations, and a layered material approach is included for the elastoplastic analysis to allow for variation of plasticity through-the-thickness. Doubly curved 20, 28, and 36 degree-of-freedom finite elements are defined based on specialization of the theory to spherical coordinates. The computer program includes algorithms for …