Ole Thybo Thomsen

Analysis of Adhesive Bonded Joints: A Unified Approach

Abstract This paper presents a newly developed unified approach for the analysis and design of adhesive bonded joints. The adherends are modelled as beams or wide plates in cylindrical bending, and are considered as generally orthotropic laminates using classical laminate theory. Consequently, adherends made as asymmetric and unbalanced composite laminates can be included in the analysis. The adhesive layer is modelled in two ways. The first approach assumes the adhesive layer to be a linear elastic material and the second approach takes into account the inelastic behaviour of many adhesives. The governing equations are formulated in terms of sets of first order ordinary differential equations. The multiple-point boundary value problem constituted by the differential equations together with the imposed boundary conditions is solved numerically by direct integration using the ‘multi-segment method’ of integration. The approach is validated by comparison with finite element models and a high-order theory approach.

Theoretical and experimental investigation of local bending effects in sandwich plates

Abstract This paper presents the results of a combined theoretical and experimental investigation of local bending effects in a clamped circular foam-cored sandwich plate subjected to a central point load. The theoretical investigation was conducted using an approximate method of local bending analysis, where the basic approach is to consider the deflection of the loaded face as being governed by a two-parameter elastic foundation model, which takes into account the existence of shearing interaction effects between the loaded face and the core material. The experimental investigation was conducted using a holographic interferometry technique, from which detailed information about the displacement field of the loaded face was obtained. Comparison between the theoretical and experimental displacement fields revealed a very convincing agreement, thus showing that the simple elastic foundation approach provides a good description of the local bending phenomenon.

Localized bending effects in sandwich panels: photoelastic investigation versus high-order sandwich theory results

Abstract The problem of local bending in sandwich panels with a ‘soft’ core often encountered in laterally loaded sandwich panels is investigated by conducting a series of photoelastic experiments. The experimental results are compared with analytical results obtained using the high-order sandwich panel theory (HSAPT). The experimental set-up consists of a symmetrically supported sandwich beam in three-point bending. The skins and the core of the sandwich specimens are made from optically active i.e. temporary double refractive, epoxy resin and polyurethane rubber, respectively, giving a elastic modular ratio of about 1260. The investigation includes two specimens differing from each other only by the thickness of their skins. The results of the analytical and experimental studies reveal that severe local stress concentrations are induced in the near vicinity of the support points and the point of external load application. The comparison between the analytical and the experimental results is presented in the form of contour line maps through the entire length and depth of the core material, and at the upper and lower fibres of the skins. The comparative study demonstrated a very good agreement between the photoelastic measurements and the predictions based on the HSAPT.

Analysis of local bending effects in sandwich plates with orthotropic face layers subjected to localised loads

Abstract This paper presents a method for the approximate analysis of local bending effects in sandwich plates with specially orthotropic face layers subjected to localised external loads. The local bending analysis is based on the assumption that the relative deflection of the loaded face against the deflection of the face not loaded can be modelled by application of an elastic foundation model. This is achieved by introducing a two-parameter elastic foundation model which takes into account the shearing interaction effects between the loaded face and the core material. An approximate solution to the complete problem is achieved by superposition of the local solution and an overall solution derived by application of classical sandwich plate theory. The results obtained are compared with finite element analysis results, and a good match between the solutions is observed. Finally a brief parametric study shows that the local bending effects are strongly influenced by the modular ratio and the thickness of the loaded face.

Sandwich Materials for Wind Turbine Blades — Present and Future

Wind turbine blades are being manufactured using polymer matrix composite materials, in a combination of monolithic (single skin) and sandwich composites. Present day designs are mainly based on glass fiber-reinforced composites (GFRP), but for very large blades carbon fiber-reinforced composites are being used increasingly, in addition to GFRP by several manufacturers to reduce the weight. The size of wind turbines have increased significantly over the last 25 years, and this trend is expected to continue in the future. Thus, it is anticipated that wind turbines with a rated power output in the range of 8—10 MW and a rotor diameter about 170—180 m will be developed and installed within the next 10—15 years. The article presents an overview of current day design principles and materials technology applied for wind turbine blades, and it highlights the limitations and important design issues to be addressed for up-scaling of wind turbine blades from the current maximum length in excess of 61 m to blade lengths in the vicinity of 90 m as envisaged for future very large wind turbines. In particular, the article discusses the potential advantages and challenges of applying sandwich type construction to a larger extent than is currently being practiced for the load-carrying parts of wind turbine blades.

Analysis and design of sandwich plates with inserts—a high-order sandwich plate theory approach

Abstract Sandwich structures are very susceptible to failure due to local stress concentrations induced in areas of load introduction, supports, geometrical and material discontinuities. These local stress concentrations are caused by localised bending effects, where the individual face sheets tend to bend about their own middle surface rather than about the middle surface of the sandwich. This paper deals with such local effects seen around inserts in structural sandwich plates. A high-order theory for bending of sandwich plates, developed and adapted especially for the purpose of studying sandwich plates with inserts and other “hard points”, is introduced. The theory, which accounts for the transverse flexibility of the core material, includes separate descriptions of the face sheets and the core materials as well as general specification of loads and boundary conditions. The theory is formulated in terms of first-order partial differential equations, which are solved numerically using the “multi-segment method of integration”. Examples involving sandwich plates with “through-the-thickness” inserts subjected to axisymmetric and non-axisymmetric external loading are presented. The paper is concluded by a discussion of design aspects.

Sandwich plates with ‘through-the-thickness’ and ‘fully potted’ inserts: evaluation of differences in structural performance

Abstract A high-order sandwich plate theory, which includes the transverse flexibility of the core, is introduced. The theory includes separate descriptions of the face sheets and the core material, and general specification of loading and boundary conditions. The theory has been adapted especially for the analysis of sandwich plates with hard points in the form of inserts, and special attention is focused on the problem of sandwich plates with inserts of the ‘through-the-thickness’ and ‘fully potted’ types. The governing equations are formulated as a set of coupled first-order differential equations, which are solved numerically using the ‘multi segment method’ of integration. Numerical results obtained for sandwich plates with ‘through-the-thickness’ and ‘fully potted’ inserts subjected to out-of-plane loading are presented. Special emphasis is focused on describing the active load transfer mechanisms, and it is demonstrated that insert/potting and potting/honeycomb interaction effects play an important role in the build-up of local stress concentrations. A detailed comparison of the results obtained for ‘through-the-thickness’ and ‘fully potted’ inserts is presented, and it is shown that the mechanical response for the latter insert type generally exhibits much more severe stress concentrations than is the case for the first insert type. The paper is concluded with a discussion of design aspects including a few guidelines for design.

Local effects across core junctions in sandwich panels

Sandwich beams and panels with symmetric faces and cores of varying stiffness are investigated. The paper presents a theoretical and experimental study of the local effects that occur in the vicinity of intersections between cores of different stiffness in such sandwich panels. These local effects manifest themselves by a significant rise of the bending stresses in the faces in the vicinity of the core junctions. Closed-form estimates of the stress/strain fields induced by local effects are presented for sandwich beams and panels loaded in cylindrical bending. The accuracy of the derived closed-form estimates is verified experimentally for the case of a sandwich beam in three-point bending.

Elasto-static and elasto-plastic stress analysis of adhesive bonded tubular lap joints

Abstract The problem of an adhesive bonded lap joint between two dissimilar orthotropic circular cylindrical laminated shells is considered. The principal directions of orthotropy do not have to coincide with the principal directions of curvature, and the external loads are allowed to be of non-axisymmetric type. The adhesive layer is modelled in two ways. The first approach assumes the adhesive layer to behave as a linear elastic material. The second, more realistic approach takes into account the predominantly inelastic behaviour of many polymeric adhesives, and it is shown that the non-linear behaviour affects the adhesive stress distribution even at low levels of external loading. The developed numerical solution procedures have been used to conduct a parametric study, and a few general design recommendations are given.

Ply drop-off effects in CFRP/honeycomb sandwich panels : Theory

This paper introduces a simple method for engineering analysis of ply drop-off induced local bending effects in CFRP/honeycomb sandwich panels. The model constituent parts are the base-line face laminate of a CFRP/sandwich panel, a dropped sub-laminate, a supporting honeycomb core material, and an adhesive/resin layer interfacing the laminates. The interaction between the core material and the face laminates is modelled using a two-parameter elastic foundation model. Two examples are evaluated, and it is shown that the elastic response is strongly influenced by the presence of a supporting core material. The results of a brief parametric study are presented, and it is demonstrated that the ply drop-off problem is influenced significantly by the out-of-plane stiffness of the honeycomb core, by the bending stiffness of the base-line face laminate and finally by the bending stiffness of the dropped sub-laminate. The paper is concluded by a discussion of design aspects.