1 DESIGN AND CONSTRUCTION OF NEW HONEYCOMB SANDWICH PANELS USING SUPERPLASTIC FORMING AND VACUUM FORMING TECHNIQUE A THESIS Presented to The Faculty of the Division of Graduate Studies by' Amilcar Jose' Gomez Fermin In Partial Fulfillment f of the Requirements for the Degree Doctor of Philosophy in the School of Mechanical Engineering Georgia Institute of Technology December, 1976
2 DESIGN AND CONSTRUCTION OF NEW HONEYCOMB SANDWICH PANELS USING SUPERPLASTIC FORMING AND VACUUM FORMING TECHNIQUE Approved: ^ / t n JI I I) ^ / ^ i /?///? ^ /? =p tr v Ac Date Approved by Chairman: \1 f)ec, \j!l
3 11 ACKNOWLEDGMENTS, The author wishes to express his deepest gratitude to Dr. John T. Berry, Chairman of the Reading Committee, academic and thesis advisor, for his encouragement, suggestions, and helpful almost weekly discussions. Deep appreciation is also expressed to Dr; Ervin E. Underwood, who gave great encouragement to the author in his graduate studies, suggested the research subject material, and the preliminary effqrts to make the wire reinforced honeycomb were under his advisorship. Special thanks are given to Dr. Charles E. Ueng who was very helpful in the preparation of a joint publication together with Dr. E. E. Underwood and the author about the wire reinforced honeycomb., presented in IV InterAmerican Materials Conference, Caracas, June Special thanks are due to Dr. Carl Jacobs, Dr. Satya Atluri, and Dr. Edgar E. Starke, for their effort as members of the thesis reading committee. The author wishes to express his gratitude to Tilden Clopton, William Peel, Louis Cavalli, Clifford Bannister, and to Donald Cabe, for their valuable help in the construction of the equipment and the conduction of the experiments. The author extends his gratitude to Mr. Olin Dewberry from the Industrial Design Department for his cooperation
4 Ill in the vacuum forming process; and to Mr. Thomas Mackrovitch for his suggestions about the heating equipment, and willingness to help. A feeling of indebtedness is expressed to the students Kim Fulkerson, Bud Rosenbach, Sudas Atvur, Richard Schmit, Trot Hunt, Jaime 0. Constain, and Marco Chiappina, for their help in relation to this thesis, as part of their requirements in the courses ME 3213 and ME 4085 in the School of Mechanical Engineering. The author extends sincere words of recognition to Sharon Butler and Annette Plunkett for their join effort in the preparation of the rough and final copies of this thesis. He wishes to express his gratitude to his wife and their children to whom this thesis is dedicated for their understanding and encouragement. A final note of gratitude goes to his parents who although they had little money; sought to raise eight children with love and help them play their roles in society.
5 TABLES OF CONTENTS Page ACKNOWLEDGMENTS ii LIST OF TABLES '.. vi LIST OF ILLUSTRATIONS viii SUMMARY ; xiii NOMENCLATURE X V Chapter I. INTRODUCTION V. 1 II. LITERATURE REVIEW Sandwich Construction Bonding Reinforcing Fibers Superplastic Materials III. INSTRUMENTATION AND EXPERIMENTAL APPARATUS.. 17 Vacuum Forming Machine Forming Die Pressure Forming Furhac» The.Instron Universal Testing Machine The Sanborn Strain Recorder Compression Shear Test Apparatus Tension Shear Test Appciratus Bending Test Apparatus Buckling Test Fixture Fixture for Four Edges Simply Supported Test IV. THEORETICAL ANALYSIS She^et Forming 2-D Friction Restricted Forming Two Dimensional Friction Free Forming 3-D Symmetric Forming Forming Time Sandwich Stress Analysis Sandwich Bending and Buckling Behavior The Core Young's Modulus Case a: Ey Case b: E..
6 V Page Case -c:.' E' Core Shear Modulus Significance of Core Mechanical Properties V. EXPERIMENTAL PROCEDURES AND RESULTS..... ; 11.0 The Plastic Wire Reinforced Honeycomb The Zn-22A1 Wire Reinforced Honeycomb (WRH) The Shear Test Heat Welding Variables The Four Point Bending Test The Two Edge Simply Supported Buckling Test The Four Edge Simply Supported Buckling Test Core Thickness Distribution VI. ANALYSIS OF DATA AND DISCUSSION Vacuum Forming Variables The Pressure Forming Variables The Shear Test The Four Point Bending Test The Two Edge Simply Supported Buckling Test The Four Edges Simply Supported Test Core Thickness Distribution VII. CONCLUSIONS AND RECOMMENDATIONS APPENDICES A. CORE MECHANICAL TEST DATA B. CORE THICKNESS DISTRIBUTION DATA C. SHEET PROPERTIES AND FORMING CONDITIONS D. APPLICATION AND SELECTION OF BONDING MEDIUM E. THE STRAIN GAGE F. SUPERPLASTICITY REFERENCES VITA.'
7 LIST OF TABLES Table Page 1. Compression Shear Test.. ' Compression Shear Test Tensile Shear Test Tensile Shear Test... ' Beam Subjected to Pure Bending Bending Test of Sandwich Beams.."' ' Buckling Test Data '' Four Edge Simply Supported Sandwich Beam Four Edge Simply Supported Sandwich Beam Four Edges Simply Supported Buckling Test Thickness Distribution Ratio in HIP w/o Wires ' Thickness Distribution Ratio in HIP with WXJL CO o n «-L. ^ ^ 13. Thickness Distribution of HIP With Wires in Square Pattern..... « Thickness Distribution Ratio of Zn-22A1 Forms Thickness Distribution Ratio of Zn-22A1 Sheets Comparison of HIP Cores Against Conventional Cores Characterization of Vacuum Forming Mechanical Properties of HIP Heat Welding of Flat Polystyrene
8 vii Page 20. Shear Test of Flat Heat Welded Specimen Heat Welding of Semicores Observations Relation Between Pressure, Thickness and Forming Time Adhesive AFEPOXY 2 Shear Test Behavior
9 Figure LIST OF ILLUSTRATIONS Page 1-1 Wire Reinforced Honeycomb (WRH) Cores'.' Schematic Representation of Vacuum Forming Machine Pressure and Vacuum Forming Die Pressure Forming Furnace The Instron Universal Testing Machine The Instron Universal Testing Machine Compression Accessory Full Bridge Connections to Carrier Preamplifier Operation of Sanborn Carrier Preamplifier Model Compression Shear Test Apparatus Tensile Shear Test Apparatus Bending Test Apparatus Buckling Test Fixture Fixture for Four Edges Simply Supported Test Forming Conditions Models for 2-D Forming,.... i D Friction Restricted Forming Steps; in 2-D Forming Force Balance of Element Under Restricted Stretching Second Forming Step Third Forming Step... 50
10 IX Figure Page 4-8 Beginning of the Second Forming Step Third Forming Step.. « Initial and Final Position of Punch (a) Intermediate Deformation Stage (b) Free Body Diagram Deformation During Forming Sheet Formed Under the Action of Tension and Pressure. « Small Equal Elements Subjected to Different External Pressures Forming Around a Projection Deflection w(x, y) of a loaded Sandwich XT Gl XI6 J- * «* *.. i Simply Supported Sandwich Plate Loaded Edgewise Sandwich Under the Action of a Tensile Load Wire Reinforced Core Different Modes of Loading in the xy Plane Loading a Core in the y Direction Sandwich Core Loaded in the x Direction Stress State Diagram ' Displacement Model to'predict G Core Under Shear Core Geometry Simply Supported Sandwich Beam Equilibrium Diagram Edgewise Loaded Simply Supported Plate.'.... \ 103
11 Figure Page 4-30 Loading of a Simply Supported Beam Number of Flaws per Vacuum Formed Sheet Core Forming Heat Welding Steps....'.. o Core Bonding Forming Time vs Applied Pressure Shear Stress vs Shear Strain of Sandwich with a WRH Polystyrene Core..» Shear Stress vs Shear Strain of Sandwich with WRH Polystyrene Core..» Shear Stress vs Shear Strain of Sandwich with WRH Polystyrene Core Heat Welding Die....» Shear Stress vs Apparent Shear Strain a Sandwich with a WRH Zn-22A1 Core.,... * Upper Portion of Tensile Shear Test in a Sandwich with WRH Zn-22A1 Core Typical Tensile Shear Test Heat Welded Specimens Bond Shear Strength vs Heat Welding Time Shear Strength of Bond vs Heat Welding Time Tensile Strength and Yield Point of HIP vs Heating Time Modulus of Elasticity of HIP vs Heating Time Four Point Bending Test Sandwich Beam Behavior Under Pure Bending Sandwich Beam Behavior Under Pure Bending.. 139
12 xi Figure Page 5-21 Two-Edge Simply Supported Buckling Test Buckling Force vs Strain in a Sandwich Beam with a WRH Zn-22AlCore Simply Supported Sandwich Beam Loaded Edgewise ' " Four Edges Simply Supported Buckling Test Wrinkling of a Sandwich Facing Under Compression Loading Several Cross Sections of the WRH Cores Thickness Distribution Ratio w/wo in HIP Forming With No Wires Thickness Distribtuion Ratio w/wo of HIP in WRH Cores Along Paths 1 and 4* Thickness Distribution of HIP Formed in a Square Pattern with Wireis Embedded Thickness Distribution of a Zn-22A1 Sheets Pressure Formed with no Wires Embedded Thickness Ratio w/wo for Zn-22A1 Sheets with Wires Embedded in a Triangular Pattern Shear Modulus for Non-Metallic Cores Shear Strength for Non-Metallic Cores Projection Arrangement in the WRH Core Internal Stresses in the Forming Process Various Wire and Projection Arrangement A-l Upper Portion of Tensile Shear Test in a.. Sandwich with WRH High Impact Polystyrene A-2 Bending Test Characteristic Curve C-l Typical Shear Test of Heat Welded HIP Specimens as Welding Time is Changed
13 xii Figure D-l D-2 E-l Page Selection of Adhesive for Core-Loading Plate Bond....., V Shear Strength of Adhesive AFEPOXY Characteristic Curve of Strain Gage Used in Bending and Buckling Tests Q
14 xiii SUMMARY The conventional light weight sandwich structure with a honeycomb core is very weak and unreliable at the fillet bond in the core-facing interface. The manufacturing method of the honeycomb is expensive, and thick cores are also very susceptible to buckling. Analytical and experimental investigations were carried out to design and construct a new core using the vacuum ore pressure forming technique, in such a way that (a) more area is available for the core-facing bond, (b) inexpensive heat welding can be used for the core bonding, and theoretically (c) the core medhanical properties are not sensitive to buckling and independent of core thickness. The optimum conditions for maximum shear strength and modulus of rigidity, the core mechanical properties, and the material flow in the various stages in the forming process were investigated, and theoretical estimates developed in this research program. Cores from both superplastic eutectoid Zn-22A1 and High Impact Polystyrene sheets, with Kevlar fibers embedded were manufactured and tested under shear, buckling, and bending; and the results were evaluated accordingly. The High Impact Polystyrene cores, although in the experimental phase, have comparable mechanical properties
15 to the non-metallic cores, and it seems that further improvement the core. is quite possible by completely heat welding A unique and novel detail in WRH cores seems to be the formation of projections with flat top and bottoms interconnected by heat welded webs which have wires or fibers embedded within them for reinformcement. The thickness distribution within the cores was scrutinized as a function of location and a theoretical justification for the flow behavior was presented. As a consequence of this analysis, an improved projection configuration and arrangement of the wires has been introduced for future investigation.
16 NOMENCLATURE Latin Symbols A Definition (R x^)/(r^-x n ),.'./ o l o V Units dimensionless ran B b c D D 2 d E E ab/n, area per projection cross section in sheet number one cross section in sheet number two core cross section m 4 area of undeformed material per projection m 4 cross section under shear length of the core m qb (1+ pft)/(7r mnd Q ), coefficient for deflection w 2 m ratio w /w n mn dimensionless width of the core core thickness flexural rigidity Etdc/(l-v ), approximate flexural rigidity c + t, conventional sandwich thickness U + V, total energy Young's modulus of elasticity m' m' m' m' m m N-m N-m m N-m MPa E c E E x core Young's modulus of elasticity sheet modulus of elasticity core modulus of elasticity in the x- direction MPa MPa MPa
17 Latin Symbols Definition Units E core modulus of elasticity in the ^ y-direction MPa E core modulus of elasticity in the a direction MPa F loading force in the shear test N F m b /a + 1, sandwich factor dimensionless F, internal force in sheet number one N F 2 internal force in sheet number two N F normal force component in a shear test N F shear force component in a shear test N F force applied to a core sheet N F force applied to the embedded wires N f s F_/N, s shear force per projection N G facing modulus of rigidity MPa G core modulus of rigidity MPa G^ core material modulus of rigidity MPa H height of projection in mathematical model h height of experimental projections m K, (mb/a + a/mb)/(l + p [ (mb/a) 2 + 1]), sandwich parameter dimensionless k stress constant Pa k 1 ^Rr> ~ x ) ^w' constant, solution of differential equation L length of plate m I distance between projections center m.. spearation between projections, length of webs m N m
18 xvii Latin Symbols Definition Units m integer number dimensionless m strain rate sensitivity factor dimensionless N number of projections in ' " a core dimensionless N force per unit length in the x-direction N/m n integer number dimensionless P P E maximum load before plate buckling failure maximum load before plate buckling failure, assuming infinite shear modulus p applied forming pressure Pa p 1 applied pressure in sheet one Pa p 2 applied pressure in sheet two Pa Q -dm/dx, shear load N q(x) normal load per unit length N/m q coefficient in load infinite series N/m n. R maximum radius of formed sheet m o r radius of curvature m r* radius of curvature at the end of second forming stcige s length of deformed element at time t m s length of a deformed element at time t + dt s* length of deformed element at the end of second forming stage t time see N N ta m m
19 xviii Latin Symbols Definition Units t o initial sheet thickness m t.. time elapsed forming sheet one see t«corresponding time forming sheet two see U strain energy N-m U strain energy of the core N-^m U f strain energy of the facings N-m u displacement in the x-direction m V potential energy of the sandwich N-m V, potential energy due to edgewise load N-m V 2 potential energy due to normcil load q N-m V effective volume of material per P projection m v displacement in the y direction m x distance in the undeformed sheet or sandwich x n distance in sheet one at time t m i. * x^ distance in sheet two at time t m y y distance in the undeformed sheet, perperdicular to x w 2^wl rat: *- 0 m m dimensionless w displacement in the z-direction m w sheet thickness at time t m w sheet thickness at time t + dt m w o initial sheet thickness m w x sheet thickness at a distance x m
20 Latin Symbols w* w i w^o) w 2 (0) w mn w w Definitions thickness at the end of second forming step thickness of sheet number ones at time t thickness of sheet number two at time t ' m initial thickness in sheet number one initial thickness in sheet number two coefficient in the infinite series of deflection deflection due to core properties only deflection independent of core properties direction perpendicular to the sandwich facing Units m m m m m m m m Greek Symbols a Y Y zx xy yz x Definition angle between the load F and the loading plates dimens ionles s shear strain shear strain in the zx plane shear strain in the xy plane shear strain in the yz plane strain strain in the x direction strain in the y direction strain rate strain rate at position A Units dimensionless dimensionless dimensionless dimensionless dimensionless dimensionless d imen s i on1ess -1 sec -1 sect
21 Definition strain rate at position B 2 2 ir Ect/2L G, sandwich constant X(3w/3x), coefficient of slope Lagrange multiplier friction coefficient li (3w/3y), coefficient of slope Poisson's ratio 7r 2 Etc/2 (1-v 2 ) Gb 2, sandwich parameter material density core density internal stress Units -1 see dimensionless dimensionless m dimensionless dimensionless dimensionless d imen s i on1e s s gr/cm gr/cm Pa internal stress in sheet number one at time t, internal stress in sheet number two at corresponding time t 2 internal stress at point A internal stress at point B Mz/DE f, stress at the facing stress in a section normal to the x-direction stress in a section normal to the y-direction shear stress f s /A, average shear stress at a section A-A in the core shear stress in a plane normal to the x direction, and oriented in the y direction Pa Pa Pa Pa Pa Pa Pa Pa Pa Pa
22 XXI Greek Synibols ft Definition (m b /a ) '+ n, sandwich parameter Units dimensionless
23 CHAPTER I INTRODUCTION The need for faster air transportation with greater effective load per pound of thrust led to the development of the sandwich construction having a very light core bonded to a strong facing on each side. The most currently used cores are made from aluminum foils, glass reinforced plastic, polyurethane or other foams, balsa wood, and paper honeycombs. Although it possesses good shear strength T and modulus of rigidity G, the conventional core requires a fillet bond to secure it to the facing sheets. This results in a decrease in reliability arid core mechanical properties, especially under fatigue. As the honeycomb cells have no internal surfaces parallel to the facings, they are extremely susceptible to buckling and the shear strength is drastically reduced in the thicker core range. Finally, the manufacturing method of the honeycomb requires an excessive amount of expensive, consecutive bonding and curing operations, rendering its use prohibitive in a number of applications. Balsa wood and paper are excellent core materials in terms of strength to weight ratio, but their properties are very unreliable and susceptible to drastic changes as
24 function of the moisture content and aging. In an attempt to improve the weak fillet bond of the standard honeycomb, plastic cellular cores have been recently introduced in the market. They are frequently manufactured by transforming heated plastic sheets into three dimensional shells possessing flat tops and bottoms; however, they do not have cells interconnected and this is very detrimental to the shear strength and the modulus of rigidity of the core. A critical evaluation of the manufacturing methods and mechanical properties of the commercial cores led to the recognition of the following principal areas which were the object of the present research: (1) Improvement of the core facing bonding areas, (2) Development of a core resistant to buckling, and (3) Methods to reduce adhesive bonding operations. Starting from this frame of reference, the author developed an apparently novel core manufacturing technique*, by which a strain rate sensitive plastic or metallic sheet can be formed around wires or fibers and projections disposed in different arrangements, as the sheets are heated to a characteristic temperature and formed by either vacuum or pressure against a die. In this way, a composite shell is generated, having the appearance *A patent covering this technique has recently been filed.
25 3 of a wire reinforced honeycomb (WRH) core, incorporating a group of surface of revolution projections disposed in a regular fashion and interconnected by vertical webs in which wires are embedded. The core presents flat tops and bottoms, as shown in Figure il-'l, which permits a good bonding area and limits the cell height to a fixed value, making the core insensitive to buckling, unlike the conventional honeycomb. The most effective bonding method, in applying the WRH process to plastic sheets, seems to be heat welding, since no adhesive is required except for bonding the core ' to the facings. Heat welding not only optimizes the core strength, but as the energy required has already been transmitted to the material for the forming process, heat welding may be economically highly advantageous. As the technique of the WRH cores was mastered, new ideas were generated up to optimize the core shear strength and the modulus of rigidity. So, in the second phase of the investigation, formulations were developed (a) for the thickness distribution in the various stages of the forming process, (b) for the optimum flow, and (c) for estimating the core mechanical properties. A series of shear, buckling, bending and thickness distribution tests were conducted in an'attempt to determine the core mechanical properties and to confirm the theoretical analysis.
26 Heat welded cores can be manufactured in a wide density range, and strength to weight ratios would be expected to increase markedly through further improvement of core-facing bond, the use of other plastics materials, and optimization of projection shape and arrangement, following the lines discussed in the present work. NODES WITH FLAT TOPS HEAT WELDED INTERCONNECTING- WEBS F^JFLAT VALLEY PROJECTIONS STRAPPED REINFORCING WIRES Figure 1-1. Wire Reinforcing Honeycomb (WRH) Cores Made from Plastics or Metallic Sheets.
27 CHAPTER II LITERATURE REVIEW To process and characterize the wire reinforced honeycomb, it is in order to make a literature survey referring to the conventional honeycomb manufacturing process, to materials currently used in sandwich construction, and to the mechanical behavior of those materials, such as polymers and superplastic Zinc-22Al which might be used for processing wire reinforced honeycomb. The following literature survey therefore relates to previous studies pertaining to sandwich construction characterization and testing procedures, bonding methods, reinforcing fibers, as well as superplastic materials. Sandwich Construction Sandwich construction is a relatively novel structural element, having its origin during World War II. It has principally been used in the air and space vehicles. Although of fairly recent origin, many researchers have devoted effort to the characterization of the mechanical properties of the light weight structures, and have attempted, for design purposes, to understand the behavior of the core as a function of configuration and materials properties.
28 " 6.- Most of the work to date has dealt with aluminum honeycomb, which seems to be the type of core most currently used. For example, Kuenzi [2,3,5,7,8], Voss , Stevens [6,7], and Jenkinson [5,10], have all been productive in the study of the aluminum honeycomb, as well as low density cores such as those made from Kraft paper, polyimide and polyester films. Topics reviewed include the strength of the core, manufacturing processes and also test procedures. Some of these may briefly be summarized as follows. Voss  studied the mechanical properties of low density sandwich cores made out of materials such as foam resins and glass-fiber deformed mats impregnated with resins having a waffle pattern. He found wide variations in the mechanical properties for otherwise similar cores. The mechanical properties of commercially available honeycombs used in structural sandwich construction have been studied by Kuenzi . The analysis of the experimental data included methods for predicting average strength and stiffness values from basic material properties and core configuration. It is interesting to note that KUenzi reports shear modulus variations for the aluminum honeycomb as much as 500 percent. Paper honeycomb for structural building panels was evaluated by Seidl, Kuenzi and Fahey . They investigated the effect of the decay, acidity,, alkalinity and aging on the shear and compressive strength of paper cores. The weight percent of the phenolic resin, urea, and sodium
29 silicate adhesives were varied in an attempt to determine optimum proportions of base material (Kraft paper) and adhesive for core manufacturing. The use of resin impregnated paper to make sandwich cores has also been studied by Markwardt and Wood . By glueing together large numbers of flat and corrugated sheets in different configurations, a variety of combinations were made available. The sandwich panels made from this type of material has an application in building construction. Turning to metallic light weight structures, Jenkinson and Kuenzi  made a series of experiments to characterize the shear strength of aluminum honeycomb cores as a function of core thickness. They found that (1) tension and compression shear tests generate similar values for shear strength and (2) as the core thickness increases the shear strength decreases for the same honeycomb density. An evaluation of the compressive and shear propertiesof corrugated foil sandwich cores was performed by Stevens . The crossbanded cores were tested and compared with conventional aluminum honeycomb for the same density. The aluminum hexagonal honeycomb proved to have higher modulus of rigidity G and shear strength.; Stevens and Kuenzi  also made a series of experimental determinations of mechanical properties of hexagonal honeycomb cores and proposed a series of linear empirical equations relating compressive strength to density,
30 compressive strength to shear strength and an equation correlating the shear strengths in the length and in the width directions of the core. Kuenzi  went on to discuss how a series of tests were conducted to assess the structural capability of titanium alloy sandwich construction having the facings and the honeycomb core bonded by diffusion. Results in flatwise tension and compression, edgewise compression and shear tests were presented. Turning to testing techniques, Kommers and Norris  designed an apparatus for evaluating sandwich plates where the load is applied normal to the facing as a vacuum pump is connected to an evacuated box that has knife edges where the sandwich rests. Although this is not a standardized test, it can be used in a rather convenient way to determine the shear properties of a sandwich construction. Comparison of the analytical and experimental deflection as a result of shear in the sandwich are possible using the described testing apparatus. Again, referring to polymeric materials, Jerikinson  has determined the shear strength of polyimide and polyester film honeycombs. The specimens wesre prepared by dipping the core edges in epoxy resins to form reinforcing fillets about 1.5 mm thick around the boundary of the cells. Most recently, Baldanza  made a state-of-the-art survey of plastic sandwich construction to provide general
31 9 and technical information for the designer in tank and automotive components such as vehicle bodies, fire walls, ballistic resistant panels and flotation units. He appears to favor the use of honeycomb for vehicle bodies provided that cells are filled with a suitable close cell foam. He reported that sandwich construction in general appears to have definite advantages over solid materials for ground transportation applications as it is evident from its high strength to weight ratio and stiffness factor. With the intention to fabricate a sandwich core with higher strength-to-density ratio than the aluminum honeycomb and with manufacturing technique involving no adhesive bonding, Ogden, Abraham and Taffee  developed a process for production of sandwich structures which can be formed to complex contqurs without detrimental effects at the corefacing interface. The core is made by roll-bonding Ti-6 Al-4 V alloy sheets and subsequently diffusion bonding the core to the facings. During the* bonding process the core is supported by filling the empty spaces with suitable materials that are later removed by a leaching operation, however, a more reliable method to eliminate the filler material had yet to be found. Looking at; more recent evaluations of honeycombs, Bendix Corporation  investigated the energy absorption characteristics of several types of aluminum honeycomb cores under a range of pressure and temperature conditions to
32 10 determine the feasibility of light weight structures as shock attenuators in the soft landing of space vehicles. The Bendix report seems to convey the idea that crushable materials in capsule form may be the best choice to counteract meteorite and landing impact, variation of friction with environment, and maintenance of close tolerances in the space ships. Turning to the analysis of the behavior of sandwich structures, following Reissner's theory of plates, Ueng  has developed a set of equations for the generalized forces acting on a sandwich plate. These equations together with the equilibrium equation represent a system of equations for the generalized forces and displacement variables. Ueng reported the similarity in the analysis of sandwich plates and homogeneous plates and provided an example problem to demonstrate the simplicity of his approach for special cases compared to other methods. A series of basic analyses in monograph form about sandwich structures have been compiled by both Allen  and Plantema . The theory, in its more complete form, can be considered as an extension of beam and plate theory for homogeneous materials. It was noted that the deflection of the sandwich as a result of core shear while disregarded in plate theory, it is considered quite significant in sandwich analysis.
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