They're already in university, and the primary school system is only just starting out?

Sun Yu let out a long sigh of relief, the tense muscles on his face finally relaxed, and he even showed a slight smile.

"Master, I don't know if it's just my imagination, but this solution seems much easier to understand than the last one."

He scratched his head, somewhat embarrassed, and said, "Last time, just figuring out the mathematical knowledge and methods used in that plan took me two or three days back at the company to barely understand it."

Upon hearing this, Chen Lin felt a surge of joy.

Goodness, Mr. Peng is indeed meticulous in his work.

The mathematical difficulty of this scheme is lower than that of the previous one concerning structural stability analysis.

This means that Mr. Peng can most likely find someone within the design institute to do this optimization, it just takes more time and manpower.

But he still gave the project to himself, at the maximum price for expedited consultation.

This 5,000 yuan is less of a consultation fee and more of a heartfelt gift.

Of course, Chen Lin also understood that President Peng's actions were likely driven by a deeper consideration.

This was the final on-site confirmation of my skill level before officially commencing long-term cooperation, with Sun Yu present.

What if I just got lucky last time and happened to stumble upon something I'm good at?

Chen Lin felt no displeasure at this cautious probing; on the contrary, he felt more at ease.

Working with a reliable, shrewd, and worldly-wise boss like this is the most worry-free option.

Thinking of this, Chen Lin's smile relaxed. He looked up at Sun Yu and asked casually, "Shall I begin explaining the new calculation scheme to you?"

Sun Yu was still slightly shocked by Chen Lin's abnormal speed of understanding everything after hearing it only once.

But having learned from his first experience, he quickly adjusted his mindset, nodded emphatically, and leaned forward slightly, adopting a posture of listening attentively.

Chen Lin pulled out a few blank sheets of draft paper from the side pocket of his backpack, and then took out a black ballpoint pen from his pencil case.

He placed one of the sheets of paper horizontally between the two of them, the tip of his pen hovering above the paper, and began to speak:

"Your original solutions, whether it's piecewise linear superposition or cutting the curve into finer infinitesimal elements, are all using discrete, linear thinking to approximate a continuous, nonlinear problem. I'll offer you a new solution based on calculus, which can directly consider the case where the tension changes continuously along the curve."

Before he finished speaking, his pen had already touched the paper, and lines of clear, neat formulas and symbols appeared smoothly before Sun Yu's eyes, accompanied by his steady explanation:

"First, we establish two fundamental exact differential equations."

The exact differential equation for the elongation of prestressed steel strands considering friction:

1. dP = -P * μ*|dθ| (The decrease in tensile force due to friction, where dθ is the increment of the central angle corresponding to the micro-arc segment)

2. d(ΔL) = (P * ds) / (E_s * A_p) (The elongation of the infinitesimal segment ds, based on Hooke's Law)

"Here, ds is the arc length along the steel strand curve. The relationship between dθ and ds is determined by the radius of curvature R(s) at that point."

【|dθ|=|ds|/ R(s)】

"For those parts in your design drawings that are clearly marked as standard circular arc segments, that is, the parts with a constant radius of curvature R, we can directly obtain the analytical solution of elongation considering friction by integration."

Chen Lin's wrist remained steady as the pen tip traced across the paper, writing down the final score:

[ΔL_arc =(P_start * L_arc)/(E_s * A_p *μ*θ)*(1 - e^(-μ*θ))

among them:

P_start: Tension at the starting point of the arc segment

L_arc: Length of the arc segment (L_arc = R * θ)

μ: friction coefficient

θ: Angle of wrap around the arc segment (in radians)

E_s: Elastic modulus of steel strand

A_p: Cross-sectional area of ​​the steel strand

After finishing writing, Chen Lin gently tapped the formula with the pen and emphasized to Sun Yu, who was already somewhat stunned, "Note that this formula is an exact solution obtained directly from the integration of the differential equation above. It fundamentally avoids the approximation error brought about by your traditional 'average tension method'."

That's exactly how it feels! Absolutely right!

As Sun Yu listened to Chen Lin's words, he nodded mechanically while screaming wildly in his mind.

It's that emotionless, monotone delivery, like reading an instruction manual from a script!

That's the style of a pro!

Chen Lin, of course, was unaware of Sun Yu's rich inner monologue. He picked up another sheet of draft paper and began explaining the specific calculation process:

"Based on this model, the overall calculation process can be divided into four steps."

"First, data preprocessing. The center line of the prestressed steel strands in the design drawings, whether it is a straight line, an arc or a transition curve, is precisely discretized into a series of sufficiently dense coordinate points (x_i, y_i, z_i)."

"Second, calculate the geometric properties of the micro-segment. For any micro-segment formed by two adjacent points, we consider it as a tiny straight line segment. We need to calculate two things: first, the length ds_i of this micro-segment, which is easy; second, the instantaneous curvature κ_i at the location of this micro-segment, and the corresponding radius of curvature R_i = 1/κ_i. This is the key, and can be achieved through the three-point method of defining a circle or more advanced differential geometry methods."

"Third, the core step, is the calculation of tension transfer. We start from the tensioning end, assuming the initial tension is P₀. Then, we perform iterative calculations for each micro-segment i:"

Chen Lin continued writing at a rapid pace, clearly and logically categorizing the cases as follows:

If the micro-segment lies within a straight line segment (κ_i≈ 0):

P_end_i = P_start_i (ignoring minor frictional losses)

ΔL_i =(P_start_i * ds_i)/(E_s * A_p)

If the micro-segment lies within the curve segment (κ_i > 0):

1. Calculate the central angle increment corresponding to the micro-segment: dθ_i≈κ_i * ds_i (because dθ= ds / R =κ* ds)

2. Calculate the tensile force attenuation using an accurate friction model: P_end_i = P_start_i * e^(-μ*|dθ_i|)

3. Apply the precise elongation formula (micro-segment version): ΔL_i =(P_start_i * ds_i)/(E_s * A_p *μ*|dθ_i|)*(1 - e^(-μ*|dθ_i|))

Then, the initial tension P_start_{i+1} = P_end_i for the next micro-segment, and so on.

"Fourth, and final, is to sum up the total elongation. ΔL_total = ΣΔL_i, which is the final result by adding up the elongation of all the micro-segments."

After explaining the four main steps, Chen Lin paused, picked up the lemonade on the table, took a sip to moisten his throat, and continued, "The advantage of this solution is that it can not only handle standard straight lines and arcs, but also any oddly shaped spatial curves you encounter in the future, such as transition curve segments. It can handle them all in one go, as long as you can provide the curvature κ(s) of each point on the curve. Moreover, its core calculation process is also a single traversal, so the computational load should not be much different from your traditional methods."

He paused, then added, "Theoretically, this algorithm can be implemented very quickly using Python. However, I've only just started learning programming and am not very proficient yet. I might have to trouble your company's programmers to implement the code based on the flow and formulas I've provided."

After he finished speaking, he noticed that Sun Yu next to him had once again fallen into a daze, staring intently at the draft paper, motionless.

Chen Lin stretched out his hand and waved in front of him.

Sun Yu jolted awake and snapped back to reality.

His momentary lapse in concentration wasn't because he didn't understand Chen Lin's plan. Since the last consultation and his conversation with General Manager Peng, he had developed an almost blind trust in Chen Lin's mathematical abilities.

He was shocked again because during the explanation, he noticed two details that made him think deeply.

First, from beginning to end, Chen Lin did not make a single correction, pause, or alteration, whether it was the formulas or symbols he wrote on the draft paper or the technical terms he uttered. The entire process was so precise and smooth, like a supercomputer with a pre-programmed sequence, accurately outputting results.

Sun Yu thought back carefully and realized that the first consultation had been similar. However, at that time, his entire focus was on those seemingly incomprehensible mathematical methods, completely ignoring Chen Lin's inhuman performance.

Secondly, and most terrifyingly, throughout the entire explanation, Chen Lin didn't look at the computer, touch his phone, consult any materials, or even hesitate or confirm for a single second. It was as if all the profound mathematical knowledge and ingenious algorithmic processes were already imprinted in his mind, readily available and perfectly invoked at any time.

Looking at Chen Lin's handsome face, Sun Yu glanced down at the several sheets of paper filled with writing, and an idea uncontrollably popped into his mind.

These must be the protagonists depicted in those online novels or games.

As for myself, an ordinary nobody with no special background, intelligence, or appearance, I can only be content to be a roadside NPC.

Sigh, how can there be such a big difference between people who study math? Oh, wait, Chen Lin isn't even studying math; he's a humanities student!