Finite Element-Based Parametric Investigation of Load-Carrying Capacity of Thick Laminated Composite Beam for Payload Support Structures

Composite materials has created an increasing demand for structural systems that are lightweight, mechanically efficient, and capable of sustaining extreme loading and environmental conditions. Conventional metallic beams, typically manufactured from steel, aluminium and of their alloys, have been extensively used in military, missile platforms, and support structures due to their predictable isotropic behaviour and established design standards. However, metallic materials possess inherent limitations, including high density, fatigue degradation under cyclic loading, and limited capability for mechanical property tailoring. These limitations directly affect mobility, payload capacity, operational efficiency, and long-term durability in modern defence systems.

To overcome these drawbacks, Fibre reinforced composite materials have emerged as promising alternatives. Composite materials such as Carbon Fibre Reinforced Polymer (CFRP) and Glass Fibre Reinforced Polymer (GFRP) exhibit superior strength and stiffness compared to conventional materials, as reported by Ahamed et al. [1]. Their high strength-to-weight ratio enables significant mass reduction while enhancing structural load-carrying capacity. In defence applications, weight reduction directly contributes to increased payload capacity, extended mission range, improved manoeuvrability, and reduced fuel consumption. Several researchers have investigated the structural behaviour of composite beams under tensile, shear, and bending loads. Uttam and Subhas [2] described the anisotropic behaviour of laminated composites using Classical Lamination Theory (CLT). According to CLT, the global mechanical response of a laminate is governed by its stiffness characteristics, represented by the ABD matrix. Accurate evaluation of these matrices, as demonstrated by Eric and Jean [3], is crucial for predicting laminate deformation under combined loading conditions. Hao Jin et al. [4] proposed a novel method for determining the ABD matrix of woven composites and validated their results using finite element analysis (FEA). Similarly, Aditya A. Joglekar et al. [5] investigated the substitution of conventional materials with composites and employed analytical formulations of the ABD matrix, which form the basis for similar calculations in the present study. Further studies by Verma and Chariar [6] emphasized the importance of laminate stacking sequence, ply thickness, and fibre orientation in tailoring structural performance. Investigations involving modelling and finite element analysis by Pavol et al. [7] and Tiren et al. [8] have successfully captured the mechanical behaviour and response of composite structures under various loading conditions. Defence-specific applications further highlight the advantages of composite beam systems. In armoured military vehicles, the replacement of metallic structural members with composite beams has been explored to reduce overall vehicle mass while maintaining structural rigidity. Mikru et al. [9] suggested the integration of composite materials in defence systems, while Gunale and Sarang [10] demonstrated their applications across various military and aerospace domains. These studies indicate a clear transition from conventional metallic structures to advanced composite materials in modern defence engineering. Modern warfare scenarios often involve high-velocity impact and deep penetration of projectiles, necessitating advanced material modelling techniques. Dong Wook Lee [11] investigated such behaviour using nonlinear finite element analysis for composite materials. UD Carbon–epoxy prepreg composites are employed in the present study; therefore, their material characteristics and modelling approaches are of particular importance. Frosina Velichkovska et al. [12] conducted experimental investigations on carbon–epoxy prepreg composites and successfully evaluated their mechanical properties. Michelle Leali Costa et al. [13] carried out the study of Carbon–epoxy prepreg properties through rheometry for airspace system. Higher thickness composites are rare to be found in commercial used. The manufacturing of such unconventional laminae is possible in composites having GSM Fabrics 1-3 mm per ply like multiaxial stitched glass fabrics.

The present study investigates the feasibility of replacing conventional metallic beams with composite beams having higher thickness laminae for payload support applications. The comparative analysis is conducted to ensure accurate stiffness characterization and to evaluate the structural suitability of composite beams for future implementation in advanced defence systems. Although commercially manufactured composites have laminae thickness of order 0.1 mm or less, this study extends the investigation to thicker laminas, preferably greater than 2 mm, to assess their load-carrying capacity under static loading conditions. The manufacturing processes and practical constraints associated with such thick composite laminates are beyond the scope of the present work; only their structural performance and load-carrying capability are evaluated.

2. Mathematical formulations

2.1 Classical Lamination Theory

The mechanical behaviour of laminated composite is governed by the anisotropic properties of individual thin plies and their stacking sequence. In the present study, an orthotropic UD carbon–epoxy 395 GPa prepreg laminate is modelled using Classical Lamination Theory (CLT) to evaluate their equivalent stiffness and stress–strain response under applied loading. Each lamina is assumed to be a transversely isotropic under plane stress conditions. In the principal material coordinate system (1–2 axes aligned with fibre and transverse to fibre direction), the stress–strain relationship is expressed as:

  σ1σ2τ12  Q11Q120Q21Q22000Q66  ε1ε2γ12                                                   (1) 

Where Q= Q11Q120Q21Q22000Q66  is called reduced stiffness matrix with Qij as the reduced stiffness coefficients. σ1,σ2 ,τ12 , ε1,ε2  and γ12  are stresses and strain in the lamina of laminated composite respectively. Further, Q11=E11-μ12μ21 ,Q12=μ12E21-μ12μ21, Q21=μ21E11-μ12μ21 _, Q22=E21-μ12μ21  _, Q₆₆  = G₁₂ , where, E₁ is longitudinal Youngs modulus (in direction 1), E₂ is transverse Youngs modulus (in direction 2), μ₁₂ is Major Poisson’s ratio  and G₁₂ is in-plane shear modulus (in plane 1-2) of lamina.

Q11 = Q₁₁ c⁴ + Q₂₂ s⁴ + 2(Q₁₂+ 2Q₆₆) s²c²,     Q12  = (Q₁₁ + Q₂₂ - 4Q₆₆) s²c² + Q₁₂ (s⁴ + c⁴)

Q22 = Q₁₁ s⁴ + Q₂₂ c⁴ + 2(Q₁₂ + 2Q₆₆) s²c²,    Q16  = (Q₁₁ - Q₁₂ - 2Q₆₆) c³s - (Q₂₂ – Q₁₂ – 2Q₆₆) s³c

Q26 = (Q₁₁ - Q₁₂ – 2Q₆₆) s³c - (Q₂₂ – Q₁₂ -2Q₆₆) c³s,  Q66 = (Q₁₁ + Q₂₂ -2Q₁₂ -2Q₆₆) s²c² + Q₆₆ (s⁴ + c⁴)

Where, c= cosθ , s=sinθ  and θ  is angle of each lamina between their material axes and global axes as Shown in figure 1. When the laminate is subjected to a force or moment, the resultant forces and moments can be written in terms of the midplane strains and curvature as

NM = ABBD  ε0k                                           (2)

Where, N denotes the forces, M denotes the Moments, ε0  is midplane strain and k is mid-plane curvature. Defining A, B and D matrices,

  Aij=k=1nQijk(Z _k - Z _k-1)    Pa.m                                                       

Bij=12k=1nQijk(Z2 _k - Z2 _k-1) Pa.m²                                                  

Dij=13k=1nQijk(Z3 _k - Z3 _k-1) Pa.m³

NxNyNxyMxMyMxy =A11A12A16B11B12B16A12A22A26B12B22B26A13A26A66B16B26B66B11B12B16D11D12D16B12B22B26D12D22D26B16B26B66D16D26D66εx0εy0γxy0kxkykxy              (3)

Here N and M with subscripts x, y and xy denoted forces and moments in that direction respectively. Same for the midstrain ε0  and curvature k . Further, the Strain calculation using below relation yields midstrain and curvature values,

ε0k = ABBD-1NM                                                                   (4)

The strain at any distance z from midplane in the laminate is calculated using below relation.

   εxεyγxy = εx0εy0γxy0  + z kxkykxy                                                                 (5)

Then Principal strains and stress in lamina making an angle θ  are calculated as,

ε1ε2γ122  = Tθ  εxεyγxy2 ,     σ1σ2τ12  = Q  ε1ε2γ12                                                 (6)

 Where T is transformation matrix, Tθ = c2s22scs2c2-2sc-scscc2-s2

2.2 Maximum Principal stress theory

According to Maximum stress theory, failure in a lamina occurs when any of the principal stresses exceeds the corresponding allowable strength of the material in that direction. i.e.

σ1maxT < σ1uT  ,  σ1maxC < σ1uC

σ2maxT <  σ2uT  ,  σ2maxC < σ2uC

(τmax ) < (τu )

σmax   and  τmax  are maximum normal and shear stress in a lamina respectively. T and C being tension and compression respectively. U for maximum strength value fixed for a given material. if any of the above criteria is not satisfied, the lamina fails which in turn leads to failure of laminate.

3. Methodology

This study compares structural strength of carbon epoxy 395 GPa prepreg laminated composite beam to conventional steel beam in carrying Payload of different weight in two different loading modes. Other modes involve transportation or dynamic mode which is not part of this study. The configuration of beam during operation in 0 degree or static mode and 90 degree or launch mode are critical from operation point of view. The tilt beam needs to qualify in both modes for operation. During static mode, the tilt beam rest on the subframe of vehicle through front support and hinged support as shown in figure 2. On the other hand, during launch mode the weight of beam is fully supported by hinges shown in figure 3. Hence these two modes are focussed in this paper. The weight of payloads are taken based on available defence data. There is no change in length of payload and hence the CG of payload is fixed on the tilt beam for all weight of payload. The dimension and shape of tilt beam conforms to defence industries guidelines. Maximum normal stress (6) generated in composites is compared with maximum normal stress generated in steel to evaluate maximum carrying capacity of material before failure. It is assumed that there is perfect bonding between laminas in the laminate and there is no delamination and hence only in plane normal stresses in two mutually perpendicular direction is evaluated.

        Fig. 2: Static mode of tilt beam.                          Fig. 3: Launch mode of tilt beam.

Critical FOS = min (FOS₁, FOS₂) in both modes. Here σmax  is maximum stress (1, 2 being in fibre or transverse to fibre direction) in any of the lamina at any location within lamina in a laminate. FOS₁ is the Factor of safety along fibre direction and FOS₂ is Factor of safety transverse to fibre direction. A new parameter called weight ratio (7) is defined. It is used to compare the strength of tilt beam of two different materials in carrying payload. it indicates carrying capacity of payload per unit weight of tilt beam.  An assumption of FOS greater than 1.5 is consider to be safe hence any loading mode of tilt beam giving FOS below this cut-off 1.5 is not accepted and unsafe for payload. The Finite Element analysis is carried out in Ansys Workbench and Ansys ACP pre/post module. Analytical results for validations are evaluated using MATLAB.                    

Numerical accuracy assessment

Composite laminates are characterised by the ABD matrix, which defines their extensional, coupling, and bending stiffness properties. Once the ABD matrix is obtained, Classical Lamination Theory (CLT) is used to evaluate the stress and strain distribution in each individual layer of the laminate. This theory is suitable for thin lamina composite and using 2D elements in FEA it was made suitable for thick laminae composite as 3D elements shows interlaminar stresses. To study the behaviour of the tilt beam with greater accuracy, a symmetric laminate composite rectangular plate of comparatively high thickness made of same material as tilt beam subjected to normal loading is modelled and validated using CLT. Analytical calculations are performed to determine the ABD matrix for the given geometry and boundary conditions, and the results are verified through Finite Element Analysis (FEA) using the Ansys ACP Pre/Post module. For validation, a transversely isotropic UD carbon–epoxy prepreg laminated composite specimen of dimensions 80 × 80 × 4 mm is modelled with a stacking sequence of [0/90/90/0], consisting of four laminae of comparatively high thickness of 1 mm.

Table 1: Properties of UD carbon epoxy 395 GPa prepreg.

Q0=2.096X10110.0255X101100.0255X10110.0948X10110000.055X1011 , Q90=0.0948X10110.0255X101100.0255X10112.096X10110000.055X1011

ABBD = 4.38X10110.102X101100000.102X10114.38X10110000000.22X10110000009.84X10110.136X101100000.136X10111.839X10110000000.293X1011

ABBD  =4.3834X10110.1024X10114.994X10-704.547X10-700.1024X10114.3834X10112.4019X10-54.547X10-7-3.63X10-604.994X10-72.4019X10-50.22X101100004.547X10-709.848X10110.1365X10111.665X10-74.547X10-7-3.63X10-600.1365X10111.840X10118.003X10-60001.665X10-78.003X10-60.2933X1011

5. Geometric and Finite Element Modelling

A tilt beam is a superstructure which holds the payload during operation. It’s a shape and size optimised mechanical structure having high strength and rigidity capable of holding payload without any mechanical failure. in this study a tilt beam shown in figure 5 having thickness of 10 mm and weight 1530 kg is taken into consideration. The CAD model of tilt beam shows two vertical sections joined using rectangular cross members. The cross members act as a mechanical coupler between section of tilt beam. there are two provisions in form of hole on the tilt beam to attach payload at the front and rear without having any load on cross members and whole assembly is hinged at rear on the subframe of vehicle through bottom hole on tilt beam. as payload is placed between two vertical sections of tilt beam shown in Figure 5 and transmits all the loads of payload from attachment points to hinge points, only these two vertical sections of tilt beam are considered for analysis and cross members are excluded.

Fig. 6: Dimensions of tilt beam in mm.

Fig. 8: Loading and boundary conditions in Launch mode.

6. Numerical Results

The stresses developed in the tilt beam in conventional material and UD carbon–epoxy prepreg laminated composite are presented in the table 2. The table further illustrates the load-carrying capacity of the steel tilt beam. It is observed that the steel beam exhibits higher load-carrying capacity in both modes of operation when compared to the laminated composite. The steel tilt beam can support a maximum payload of 40 tons with min FOS of 1.583, achieving a weight ratio of 26.14.  As the payload increases, the minimum factor of safety (FOS) decreases. Data corresponding to FOS values below cut off 1.5 have not been included in the table for either the composite or steel configurations and simply shown by dash line. The accurate variation of FOS below 1.5 is depicted in Figure 13-15. The weight ratio is higher for composite materials compared to conventional steel material. For the 2-ply configuration, the stacking sequence [0/0], [90/90] and [0/90] achieves a maximum weight ratio of 33.33 and is suitable for carrying a payload upto10 tons. The stacking sequence [0/0] and [0/90] is found suitable for carrying a 12.5 ton and has weight ratio of 41.66. The maximum load-carrying capacity of the 2-ply UD carbon epoxy laminated composite is 12.5 ton. In the case of the 3-ply laminate composite, the stacking sequence [45/0/-45], [ 45/0/45], [ 90/0/90] and [0/90/0] is suitable for carrying payload upto10 ton giving maximum weight ratio of 33.33. Only [45/0/45] composite is suitable for 12.5 ton of payload with weight ratio of 41.66. for 4 ply laminate composites, stacking sequence of [0/90/90/0], [45/-45/-45/45], [0/45/-45/0] and [90/45/-45/90] is found to be suitable for 5 ton of payload with weight ratio of 16.66 and stacking sequence of [0/90/90/0] and [90/45/-45/90] for 10 ton of payload with weight ratio of 33.33. However, none of the evaluated stacking sequences are found to be suitable for higher payloads of 15 tons and more and hence the comparative study was stopped at this payload weight.

Table 3: Stress and FOS of 2 ply laminate composite tilt beam.

Table 4: Stress and FOS of 3 ply laminate composite tilt beam.

Table 5: Stress and FOS of 4 ply laminate composite tilt beam.

Fig. 12: Variation of FOS with weight in.                  Fig. 13: Variation of FOS with Weight in 2   steel Tilt beam                                                             Ply Composite Tilt beam.

Fig. 14: Variation of FOS with Weight in 3             Fig. 15: Variation of FOS with Weight in 4      Ply Composite Tilt beam.                                         Ply Composite Tilt beam.

Fig. 16: Stress in Steel tilt beam in Static mode.                       

 

 

Fig. 17: Stress in Steel tilt beam in Launch mode.

Fig. 18: Stress σ1

 distribution in [0/90/0] composite            

Fig. 19: Stress σ2

Tilt beam in static mode.                                                 composite tilt beam in static mode.

 distribution in [0/90/0] composite                      Fig. 21: Stress σ2  distribution in [0/90/0]

Tilt beam in launch mode.                                                 composite tilt beam in launch mode.