Buckling,Hygrothermal, Loop connections, Bolted joints

Calculate equilibrium forces and Moment on a deformed laminate element under inplane loads along with transverse shear forces and moments substitute them in ABD matrix we get coupled equations for unsymmetric laminate but for symmetric laminate we get uncoupled equation

3rd equation which deals with deflection in z axis or Wo or plate behaviour is considered in symmetric laminate buckling eq

Navier plate with basic Boundary conditions

Because it fulfills all given boundary conditions

Buckling load vs length

the higher m becomes the more the curves shift they open up more as m gets higher

the relevant value is the lowest one - Garland curve the lower Boundary curve is the relevant one

In local buckling of web is considered as Navier plate as Moment free support on all edges

for Flanges local buckling it is considered that the boundary conditions are quite different, the flanges are moment free in 3 edges and free support in one edge which uses rayleigh theory to solve the buckling differential equation

However, the D16 and D26 are considered in the formation of the buckling equation those are neglected because they provide weakening in regards to plate buckling, and also they are neglected in theta=0 and 90 and cross-ply laminates Bending-twisting coupling has a weakening effect on laminates under compressive load and must not be neglected in a buckling analysishowever to make the solution more conservative we need to consider eliminatoing them

we consider the wave equation which considers both u0,v0, and w0 as a boundary condition

A higher degree of unsymmetry leads to a decreasing buckling loadshould be avoided as far as possible, Strong influence of degree of unsymmetry and layer angles

Here along with Wo we also consider rotation along x and Y axis so 2 more equations arise which are then substituted in buckling equation and trivial soloutin is obtained For thick laminates a weakening effect of transverse shear deformations occurs

Et=alphaT(T-T0); Alpha t is thermal expansion

e=eM+eT

for indeterminate support (e=sigma/E+alphaT(deltaT))

Matrix material is influenced by HT

Consequences of high temperatures: − Stiffnesses, Strength properties decrease − Especially dangerous: hot + humid conditions − Compressive strength // especially affected − Creep and relaxation Increases − Moisture absorption, thermal conductivity increases − Chemicals react more aggressive − Electr. resistance decreases

sigma=Ce-AlphaTDeltaT, e=Ssigma+alphaTdeltaT

we have compressve load on fiber and tensile stress on matrix parallel to thermal expansion or load however the strsses differ like sigma mAm= Sigma f * Af

but strains remains same for matrix and fibers and we know that Alpha T= e11-/dELTA T

iNTERPRETATION OF RESULTS

Coefficient of thermal expansion depends on thermal properties of fiber and matrix and the respective stiffness properties. (The stiff fiber enforces its thermal strain onto the matrix material) - in longitudinal direction: close to . - Important factor: fiber volume fraction vf - Unfavorable thermal longitudinal eigenstresses: - Tensile eigenstresses in the matrix - Compressive eigenstresses in the fiber

fiber volume fraction and thermal expansion coefficient of matrix n fiber. Avoid large discrepancies in the orientation angles of adjacent layers.

Many materials are not impermeable → Moisture absorption − Water absorption primarily concerns the matrix −

Glass- and C-fibers do not absorb moisture −

Aramid- and bio-fibers absorb moisture − Moisture distribution strongly time-dependentt

Two kinds of moisture storage:

Between the molecule chains

in pores, cracks → condenses away

Mass increase

Dimensions increase

Electrical resistance decreases

Thermal conductivity increases

Elongation at break increases

Results in stress states

Influences the elasticity constants

Conclusion: Clear influence of temperature and moisture on stiffness and strength properties of laminates. Often neglected in practice, requires non-linear analysis. Considered in experiments by application of different environmental conditions

Obvious joint solution 2. Uses high fiber tensile strength properties 3. Punctual introduction of high stresses 4. Expensive manufacturing (requires manual work) 5. Requires tight laying of the fibers 6. Disadvantage: Inhomogeneous state of stress, fibers are not exploited evenly

basic assumptions Stresses evenly distributed over width - Rotational symmetry: No shear stresses, no variation of the state variables in the tangential direction - Friction between loop connector and bolt is neglected - No thermal of swelling stresses

2 different types of cases one with lateral support to hold th efibers and other without

Stress conc at inner radius Uneven utilization of fibers

Secondary bending stresses to be taken into account (requires numerical analysis) because of the bending of the fibers inside the loop

Sigma T leads to fiber failure but Sigma R leads to matrix failure

design: Series connection for avoidance of high ratios ra / ri

Multilayered loop connections:

Use of hybrid loops

Application of crack stoppers

types

structural bonding - structural adhesives (epoxies) strength highest

elastic bonding - Elastic adhesives strength med

sealing - sealants strength low

Adv:

Different materials can be joined - No heat influence on the parts to be joined - No notch effect as with bolt connections - Additional sealing effect - Rough tolerances possible - High damping and energy absorption

Disadv: Non-uniform stress profile, stress peaks in the adhesive - Sensitive to peel stress - Adhesives generally polymers: limitations due to temperature and humidity - Complex pretreatment of the parts to be bonded - Strong influence of production - Quality assurance is difficult - Additional weight due to overlaps

Shafting, Double lap joints, single lap joining, Doubler

as shafting angle increases relative adhesive stressess Sigma alpha/sigma x decreases and tow alpha/sigma x increases untill 45 increases and decreasses

adv-Transformation of normale stresses into tolerable shear stresses - Enlargement of the adhesive surface - No stress peaks at shafting endes - No bending moments - No doublers, optimal for lightweight design - No steps, smooth surface

disadv- complex and expensive production

Joining parts only transfer normal forces

Adhesive layer only transfers shear.

Shear flow is constant over thickness of the adhesive layer.

Ideal adhesion between joining parts and adhesive layer.

Planar joining parts and adhesive layer with constant thicknesses.

Linear elasticity, geometrical linearity. Only plane deformations, no strains in thickness direction.

Joining parts orthotropic, adhesive layer isotropic.

Bending is not considered.

Stress peak for equal joining part stiffnesses Et

Improvement: increase b

Stress distribution in the adhesive layer for different overlap lengths

shear stresses leads to peeling stresses

Joining of parts of different thickness. - Leads to unsymmetric stress distributionsStress distributions in adhesive layers of doublers:

Measeures:

Increase shear strength by simulataneous transverse compression

graded wedge shape, wedge shaped adhesion, use surplus adhesive